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Stanley Pliska

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University of Cambridge

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Université de Montréal

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Papers by Stanley Pliska

Option Valuation with Co-Integrated Asset Prices

Many financial data series are found to be co-integrated. The implications of cointegrationon opt... more Many financial data series are found to be co-integrated. The implications of cointegrationon option valuation are studied in this article, as we develop the optionvaluation theory for co-integrated price systems. We also examine the diffusion limitof the system and numerically demonstrate the co-integration effect using spread options.

$Fig. 2. Spread option values of one-year maturity (reported as fractions of the S&P500 index value) along with two-standard deviation confidence bands (based on 200,000 sample paths). The horizontal axis is the strike price ratio (the strike price divided by the S&P500 index value). The spread formula uses q = 1.1 x (Si;/Sz) and the option values are based on the assumption that the conditional volatilities equal their respective stationary volatilities.$

A 3-factor Valuation Model for Mortgage-Backed Securities (MBS)

In this paper we generalize the one-factor MBS-pricing model pro- posed by Kariya and Kobayashi(2... more In this paper we generalize the one-factor MBS-pricing model pro- posed by Kariya and Kobayashi(2000) to a 3-factor model. We describe prepayment behavior due to refinancing and rising housing prices by incentive response functions. Our valuation of an MBS is based on discrete-time, no-arbitrage pricing theory, making an association be- tween prepayment behavior and cash flow patterns. The structure, ra-

Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management

In this paper we extend standard dynamic programming results for the risk sensitive optimal contr... more In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only ®nite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the ®nancial problem of managing a portfolio of assets which are a¨ected by Markovian microeconomic and macroeconomic factors and where the investor seeks to maximize the portfolio's risk adjusted growth rate.

An Overview of Optimal Life Insurance Purchase, Consumption and Investment Problems

by Stanley Pliska and A. Pinto

Springer Proceedings in Mathematics, 2011

Abstract We provide an extension to Merton&amp;#x27;s famous continuous time model of optimal... more

The shadow price of information in continuous time decision problems

Stochastics, 1987

A three-factor valuation model for mortgage-backed securities (MBS)

Managerial Finance, 2011

Purpose – The purpose of this paper is to generalize the one-factor mortgage-backed securities (M... more Purpose – The purpose of this paper is to generalize the one-factor mortgage-backed securities (MBS)-pricing model proposed by Kariya and Kobayashi to a three-factor model. The authors describe prepayment behavior due to refinancing and rising housing prices by discrete-time, no-arbitrage pricing theory, making an association between prepayment behavior and cash flow patterns. Design/methodology/approach – The structure, rationality and potential for

Risk Sensitive Portfolio Management with Cox--Ingersoll--Ross Interest Rates: The HJB Equation

SIAM Journal on Control and Optimization, 2005

This paper presents an application of risk sensitive control theory in financial decision making.... more This paper presents an application of risk sensitive control theory in financial decision making. The investor has an infinite horizon objective that can be interpreted as maximizing the portfolio's risk adjusted exponential growth rate. There are two assets, a stock and a bank account, and two underlying Brownian motions, so this model is incomplete. The novel feature here is that the interest rate for the bank account is governed by Cox-Ingersoll-Ross dynamics. This is significant for risk sensitive portfolio management because the factor process, unlike in the Gaussian and all other cases treated in the literature, cannot be negative.

Economic Properties of the Risk Sensitive Criterion for Portfolio Management

Review of Accounting and Finance, 2003

Optimal tracking for asset allocation with fixed and proportional transaction costs

Quantitative Finance, 2004

This paper studies the asset allocation problem of optimally tracking a target mix of asset categ... more This paper studies the asset allocation problem of optimally tracking a target mix of asset categories when there are transaction costs. We consider the trading strategy for an investor who is trying to minimize both fixed and proportional transaction costs while simultaneously minimizing the tracking error with respect to a specified, target asset mix. We use impulse control theory in

Portfolio management with transaction costs

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1997

It is known that the optimal trading strategy for a certain portfolio problem featuring fixed tra... more

Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms

Optimization, 2012

We introduce an extension to Merton's famous continuous time model of optimal consumption and inv... more We introduce an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities driven by multidimensional Brownian motion. We then provide a detailed analysis of the optimal consumption, investment, and insurance purchase strategies for the wage earner whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming methods to obtain explicit solutions for the case of discounted constant relative risk aversion utility functions and describe new analytical results which are presented together with the corresponding economic interpretations.

Optimal Scheduling of Inspections: A Delayed Markov Model with False Positives and Negatives

Operations Research, 1991

Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management

Mathematical Methods of Operations Research (ZOR), 1999

In this paper we extend standard dynamic programming results for the risk sensitive optimal contr... more In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only ®nite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the ®nancial problem of managing a portfolio of assets which are a¨ected by Markovian microeconomic and macroeconomic factors and where the investor seeks to maximize the portfolio's risk adjusted growth rate.

CONTINUOUS-TIME MEAN-VARIANCE PORTFOLIO SELECTION WITH BANKRUPTCY PROHIBITION

Mathematical Finance, 2005

A continuous-time mean-variance portfolio selection problem is studied where all the market coeff... more A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.

OPTIMAL PORTFOLIO MANAGEMENT WITH FIXED TRANSACTION COSTS

Mathematical Finance, 1995

We study optimal portfolio management policies for an investor who must pay a transaction cost eq... more We study optimal portfolio management policies for an investor who must pay a transaction cost equal to a tixed fraction of his portfolio value each time he trades. We focus on the infinite horizon objective function of maximizing the asymptotic growth rate. so the optimal policies we derive approximate those of an investor with logarithmic utility at a distant horizon. When investment opportunities are modeled as m correlated geometric Brownian motion stocks and a riskless bond, we show that the optimal policy reduces to solving a single stopping time problem. When there is a single risky stock, we give a system of equations whose solution determines the optimal rule. We use numerical methods to solve for the optimal policy when there are two risky stocks. We study several specific examples and observe the general qualitative result that, even with very low transaction cost levels, the optimal policy entails very infrequent trading.

On the fundamental theorem of asset pricing with an infinite state space

Journal of Mathematical Economics, 1991

An example is given of a securities market in which there is no arbitrage and a risk-neutral agen... more An example is given of a securities market in which there is no arbitrage and a risk-neutral agent has an optimal demand subject to a minimum wealth constraint, yet there is no risk-neutral probability measure and no state price density. Also, there is no linear pricing rule on Lp for any p < a. This failure of the 'Fundamental Theorem of Asset Pricing' is due to a lack of countable additivity of the pricing operator in the market. Some suilicient conditions are also given for the existence of a risk-neutral probability measure and state price density for pricing L" claims.

A martingale characterization of the price of a nonrenewable resource with decisions involving uncertainty

Journal of Economic Theory, 1985

Option valuation with co-integrated asset prices

Journal of Economic Dynamics and Control, 2004

This paper investigates theoretical and practical aspects of options that are based upon two or m... more This paper investigates theoretical and practical aspects of options that are based upon two or more assets which are co-integrated. For this purpose, a new, discrete-time model of asset prices is developed, a model featuring both the co-integration property as well as stochastic volatilities. Using a GARCH, equilibrium-based option pricing approach, it is shown that when volatilities are deterministic the option prices do not depend on the co-integration parameters, except for the mis-speciÿcation e ect as to the manner in which the volatilities are estimated. However, with stochastic volatilities the option prices explicitly depend upon the co-integration parameters. In order to understand these results better, this paper also examines a continuous-time, di usion limit of the asset price system and empirically studies the co-integration e ect using spread options based upon the S& P500 and the NASDAQ100. These numerical results suggest that consideration of co-integration can substantially alter the value, delta and vega of a spread option. ?

$Fig. 2. Spread option values of one-year maturity (reported as fractions of the S&P500 index value) along with two-standard deviation confidence bands (based on 200,000 sample paths). The horizontal axis is the strike price ratio (the strike price divided by the S&P500 index value). The spread formula uses q = 1.1 x (Si;/Sz) and the option values are based on the assumption that the conditional volatilities equal their respective stationary volatilities.$

A synopsis of federal-state sponsored preventive child health

Journal of Community Health, 1984

This synopsis presents data on the impact of services and evaluation issues for the nation's larg... more This synopsis presents data on the impact of services and evaluation issues for the nation's largest preventive child health program, the Early and Periodic Screening, Diagnosis and Treatment program (EPSDT). The information is drawn from a series of six EPSDT demonstration/evaluation (D/E) projects sponsored by the Health Care Financing Administration between 1972 and 1979. These projects were implemented in order to learn how to provide preventive services for children participating in the Medicaid program. The results of D/E activities are revised in a methodological framework as defined by principles of epidemiology and evaluation research. Consideration of the major threats to valid interpretation of the D/E findings shows self-selection to be the most serious methodological problem. Data pertaining to the history of use of preventive services, number of children found to have problems in screening, the treatment status and subjective seriousness of these problems, and the resolution of conditions referred to diagnosis and treatment are presented within the context of this methodological critique.

Optimal life insurance purchase and consumption/investment under uncertain lifetime

by Stanley Pliska and Jinchun Ye

Journal of Banking & Finance, 2007

In this paper we consider optimal insurance and consumption rules for a wage earner whose lifetim... more In this paper we consider optimal insurance and consumption rules for a wage earner whose lifetime is random. The wage earner is endowed with an initial wealth, and he also receives an income continuously, but this may be terminated by the wage earner's premature death. We use dynamic programming to analyze this problem and derive the optimal insurance and consumption rules. Explicit solutions are found for the family of CRRA utilities, and the demand for life insurance is studied by examining our solutions and doing numerical experiments.

Option Valuation with Co-Integrated Asset Prices

Many financial data series are found to be co-integrated. The implications of cointegrationon opt... more Many financial data series are found to be co-integrated. The implications of cointegrationon option valuation are studied in this article, as we develop the optionvaluation theory for co-integrated price systems. We also examine the diffusion limitof the system and numerically demonstrate the co-integration effect using spread options.

$Fig. 2. Spread option values of one-year maturity (reported as fractions of the S&P500 index value) along with two-standard deviation confidence bands (based on 200,000 sample paths). The horizontal axis is the strike price ratio (the strike price divided by the S&P500 index value). The spread formula uses q = 1.1 x (Si;/Sz) and the option values are based on the assumption that the conditional volatilities equal their respective stationary volatilities.$

A 3-factor Valuation Model for Mortgage-Backed Securities (MBS)

In this paper we generalize the one-factor MBS-pricing model pro- posed by Kariya and Kobayashi(2... more In this paper we generalize the one-factor MBS-pricing model pro- posed by Kariya and Kobayashi(2000) to a 3-factor model. We describe prepayment behavior due to refinancing and rising housing prices by incentive response functions. Our valuation of an MBS is based on discrete-time, no-arbitrage pricing theory, making an association be- tween prepayment behavior and cash flow patterns. The structure, ra-

Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management

In this paper we extend standard dynamic programming results for the risk sensitive optimal contr... more In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only ®nite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the ®nancial problem of managing a portfolio of assets which are a¨ected by Markovian microeconomic and macroeconomic factors and where the investor seeks to maximize the portfolio's risk adjusted growth rate.

An Overview of Optimal Life Insurance Purchase, Consumption and Investment Problems

by Stanley Pliska and A. Pinto

Springer Proceedings in Mathematics, 2011

Abstract We provide an extension to Merton&amp;#x27;s famous continuous time model of optimal... more

The shadow price of information in continuous time decision problems

Stochastics, 1987

A three-factor valuation model for mortgage-backed securities (MBS)

Managerial Finance, 2011

Purpose – The purpose of this paper is to generalize the one-factor mortgage-backed securities (M... more Purpose – The purpose of this paper is to generalize the one-factor mortgage-backed securities (MBS)-pricing model proposed by Kariya and Kobayashi to a three-factor model. The authors describe prepayment behavior due to refinancing and rising housing prices by discrete-time, no-arbitrage pricing theory, making an association between prepayment behavior and cash flow patterns. Design/methodology/approach – The structure, rationality and potential for

Risk Sensitive Portfolio Management with Cox--Ingersoll--Ross Interest Rates: The HJB Equation

SIAM Journal on Control and Optimization, 2005

This paper presents an application of risk sensitive control theory in financial decision making.... more This paper presents an application of risk sensitive control theory in financial decision making. The investor has an infinite horizon objective that can be interpreted as maximizing the portfolio's risk adjusted exponential growth rate. There are two assets, a stock and a bank account, and two underlying Brownian motions, so this model is incomplete. The novel feature here is that the interest rate for the bank account is governed by Cox-Ingersoll-Ross dynamics. This is significant for risk sensitive portfolio management because the factor process, unlike in the Gaussian and all other cases treated in the literature, cannot be negative.

Economic Properties of the Risk Sensitive Criterion for Portfolio Management

Review of Accounting and Finance, 2003

Optimal tracking for asset allocation with fixed and proportional transaction costs

Quantitative Finance, 2004

This paper studies the asset allocation problem of optimally tracking a target mix of asset categ... more This paper studies the asset allocation problem of optimally tracking a target mix of asset categories when there are transaction costs. We consider the trading strategy for an investor who is trying to minimize both fixed and proportional transaction costs while simultaneously minimizing the tracking error with respect to a specified, target asset mix. We use impulse control theory in

Portfolio management with transaction costs

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1997

It is known that the optimal trading strategy for a certain portfolio problem featuring fixed tra... more

Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms

Optimization, 2012

We introduce an extension to Merton's famous continuous time model of optimal consumption and inv... more We introduce an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities driven by multidimensional Brownian motion. We then provide a detailed analysis of the optimal consumption, investment, and insurance purchase strategies for the wage earner whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming methods to obtain explicit solutions for the case of discounted constant relative risk aversion utility functions and describe new analytical results which are presented together with the corresponding economic interpretations.

Optimal Scheduling of Inspections: A Delayed Markov Model with False Positives and Negatives

Operations Research, 1991

Risk sensitive control of finite state Markov chains in discrete time, with applications to portfolio management

Mathematical Methods of Operations Research (ZOR), 1999

In this paper we extend standard dynamic programming results for the risk sensitive optimal contr... more In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only ®nite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the ®nancial problem of managing a portfolio of assets which are a¨ected by Markovian microeconomic and macroeconomic factors and where the investor seeks to maximize the portfolio's risk adjusted growth rate.

CONTINUOUS-TIME MEAN-VARIANCE PORTFOLIO SELECTION WITH BANKRUPTCY PROHIBITION

Mathematical Finance, 2005

A continuous-time mean-variance portfolio selection problem is studied where all the market coeff... more A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.

OPTIMAL PORTFOLIO MANAGEMENT WITH FIXED TRANSACTION COSTS

Mathematical Finance, 1995

We study optimal portfolio management policies for an investor who must pay a transaction cost eq... more We study optimal portfolio management policies for an investor who must pay a transaction cost equal to a tixed fraction of his portfolio value each time he trades. We focus on the infinite horizon objective function of maximizing the asymptotic growth rate. so the optimal policies we derive approximate those of an investor with logarithmic utility at a distant horizon. When investment opportunities are modeled as m correlated geometric Brownian motion stocks and a riskless bond, we show that the optimal policy reduces to solving a single stopping time problem. When there is a single risky stock, we give a system of equations whose solution determines the optimal rule. We use numerical methods to solve for the optimal policy when there are two risky stocks. We study several specific examples and observe the general qualitative result that, even with very low transaction cost levels, the optimal policy entails very infrequent trading.

On the fundamental theorem of asset pricing with an infinite state space

Journal of Mathematical Economics, 1991

An example is given of a securities market in which there is no arbitrage and a risk-neutral agen... more An example is given of a securities market in which there is no arbitrage and a risk-neutral agent has an optimal demand subject to a minimum wealth constraint, yet there is no risk-neutral probability measure and no state price density. Also, there is no linear pricing rule on Lp for any p < a. This failure of the 'Fundamental Theorem of Asset Pricing' is due to a lack of countable additivity of the pricing operator in the market. Some suilicient conditions are also given for the existence of a risk-neutral probability measure and state price density for pricing L" claims.

A martingale characterization of the price of a nonrenewable resource with decisions involving uncertainty

Journal of Economic Theory, 1985

Option valuation with co-integrated asset prices

Journal of Economic Dynamics and Control, 2004

This paper investigates theoretical and practical aspects of options that are based upon two or m... more This paper investigates theoretical and practical aspects of options that are based upon two or more assets which are co-integrated. For this purpose, a new, discrete-time model of asset prices is developed, a model featuring both the co-integration property as well as stochastic volatilities. Using a GARCH, equilibrium-based option pricing approach, it is shown that when volatilities are deterministic the option prices do not depend on the co-integration parameters, except for the mis-speciÿcation e ect as to the manner in which the volatilities are estimated. However, with stochastic volatilities the option prices explicitly depend upon the co-integration parameters. In order to understand these results better, this paper also examines a continuous-time, di usion limit of the asset price system and empirically studies the co-integration e ect using spread options based upon the S& P500 and the NASDAQ100. These numerical results suggest that consideration of co-integration can substantially alter the value, delta and vega of a spread option. ?

$Fig. 2. Spread option values of one-year maturity (reported as fractions of the S&P500 index value) along with two-standard deviation confidence bands (based on 200,000 sample paths). The horizontal axis is the strike price ratio (the strike price divided by the S&P500 index value). The spread formula uses q = 1.1 x (Si;/Sz) and the option values are based on the assumption that the conditional volatilities equal their respective stationary volatilities.$

A synopsis of federal-state sponsored preventive child health

Journal of Community Health, 1984

This synopsis presents data on the impact of services and evaluation issues for the nation's larg... more This synopsis presents data on the impact of services and evaluation issues for the nation's largest preventive child health program, the Early and Periodic Screening, Diagnosis and Treatment program (EPSDT). The information is drawn from a series of six EPSDT demonstration/evaluation (D/E) projects sponsored by the Health Care Financing Administration between 1972 and 1979. These projects were implemented in order to learn how to provide preventive services for children participating in the Medicaid program. The results of D/E activities are revised in a methodological framework as defined by principles of epidemiology and evaluation research. Consideration of the major threats to valid interpretation of the D/E findings shows self-selection to be the most serious methodological problem. Data pertaining to the history of use of preventive services, number of children found to have problems in screening, the treatment status and subjective seriousness of these problems, and the resolution of conditions referred to diagnosis and treatment are presented within the context of this methodological critique.

Optimal life insurance purchase and consumption/investment under uncertain lifetime

by Stanley Pliska and Jinchun Ye

Journal of Banking & Finance, 2007

In this paper we consider optimal insurance and consumption rules for a wage earner whose lifetim... more In this paper we consider optimal insurance and consumption rules for a wage earner whose lifetime is random. The wage earner is endowed with an initial wealth, and he also receives an income continuously, but this may be terminated by the wage earner's premature death. We use dynamic programming to analyze this problem and derive the optimal insurance and consumption rules. Explicit solutions are found for the family of CRRA utilities, and the demand for life insurance is studied by examining our solutions and doing numerical experiments.