Papers by Vittorio Moriggia
Special issue of the IMA Journal of Management Mathematics that includes selected papers presente... more Special issue of the IMA Journal of Management Mathematics that includes selected papers presented at the XIII International Conference on Stochastic Programming held in Bergamo in 2013 and the First Euro mini conference on Stochastic Programming held in Paris in 2014.
Stochastic programming approaches are increasingly adopted to address different types of financia... more Stochastic programming approaches are increasingly adopted to address different types of financial planning problems: from the classical asset-liability management problem [14] and large enterprise-wide risk management problems [13], to financial engineering applications [3] and complex portfolio management problems [2]. We discuss in this article a credit portfolio problem characterised by a complex underlying model of uncertainty [10, 1]. Increasing computational power, the ability to reach a very accurate, still manageable, representation of the decision problem and the growing evidence that for practical purposes a possibly large yet finite number of scenarios is sufficient to identify an optimal strategy are all pushing in favour of stochastic programming formulations. Financial applications, to a large extent independently from the specific financial problem, rely on a common information structure linking the optimal problem formulation to an accurate description of risk facto...
We address the problem of a private pension plan sponsor who has to decide the best pension funds... more We address the problem of a private pension plan sponsor who has to decide the best pension funds that should be offered to the pension plan members. Starting from the analysis of the population of the plan in order to identify a set of representative subscribers, we focus on an individual optimal portfolio allocation in a pension perspective. Then, the optimal allocation for each representative will become a pension fund. For each representative, we propose a multistage stochastic program (MSP) which includes a multi-criteria objective function. The optimal choice is the portfolio allocation that minimizes the Average Value at Risk Deviation of the final wealth and satisfies a wealth target in the final stage. Stochasticity arises from investor’s salary process and asset returns. The stochastic processes are assumed to be correlated. Numerical results show optimal dynamic portfolios with respect to investor’s preferences and then the best pension funds the provider can offer.
Il VOLUME A affronta le principali metodologie e le tecniche fondamentali per la progettazione e ... more Il VOLUME A affronta le principali metodologie e le tecniche fondamentali per la progettazione e la realizzazione di applicazioni software e di pagine Web. La prima parte del volume introduce i concetti di linguaggio e di automa. Si prosegue presentando le linee guida della programmazione strutturata per la progettazione degli algoritmi e infine, nel terzo capitolo, ci si concentra sulle basi del linguaggio C, come strumento per la codifica e la validazione degli algoritmi. Nella seconda parte il testo e incentrato sulle caratteristiche del linguaggio C++, di cui vengono sottolineate in particolare le analogie e le differenze rispetto al linguaggio C per quanto riguarda il lessico e la sintassi. Vengono presentati gli elementi fondamentali della programmazione ad oggetti, non soltanto a livello teorico, ma mostrando, in modo facile e intuitivo, come essa sia il paradigma che trova un’ampia applicazione pratica nello sviluppo del software moderno, basato sulle classi e sugli oggetti....
Computational Management Science
The practical adoption of the Solvency II regulatory framework in 2016, together with increasing ... more The practical adoption of the Solvency II regulatory framework in 2016, together with increasing property and casualty (PC) claims in recent years and an overall reduction of treasury yields across more developed financial markets have profoundly affected traditional risk management approaches by insurance institutions. The adoption of firm-wide risk capital methodologies to monitor the companies' overall risk exposure has further consolidated the introduction of risk-adjusted performance measures to guide the management medium and long-term strategies. Relying on a dynamic stochastic programming formulation of a 10 year asset-liability management (ALM) problem of a PC company, we analyse in this article the implications on capital allocation and risk-return trade-offs of an optimization problem developed for a global insurance company based on a pair of risk-adjusted return functions. The analysis is relevant for any institutional investor seeking a high risk-adjusted performance as for regulators in their structuring of stress-tests and effective regulatory frameworks. The introduction of the concept of risk capital, or economic capital, in the definition of medium and long term insurance strategies poses a set of modeling and methodological issues tackled in this article. Of particular interest is the study of optimal ALM policies under different assets' correlation assumptions. From a computational viewpoint it turns out that, depending on the assumed correlation matrix, the stochastic program is linear or of second order conic type. A case study from a real-world company development is presented to highlight the effectiveness of applied stochastic programming We acknowledge the cooperation of Dr. Giacomo Landoni during part of this development and the long-term cooperation with Dr. Massimo di Tria, currently Chief Investment Officer at Cattolica Assicurazioni in Italy and previously deputy Head of ALM at Allianz Investment Management. Dr.
Omega
Abstract The main goal of a pension fund manager is sustainability. We propose an Asset and Liabi... more Abstract The main goal of a pension fund manager is sustainability. We propose an Asset and Liability Management model structured as a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. Among other constraints, we consider the second-order stochastic dominance with respect to a benchmark portfolio. To protect the pension fund from shocks, we test the inclusion of hedge financial contracts in the form of put options and, moreover, we stress the portfolio introducing a new scenario tree contamination technique, namely the nodal contamination. Numerical results show that we can efficiently manage the pension fund satisfying several targets such as liquidity, returns, sponsor’s extraordinary contribution and funding gap. Moreover, we test the sensitivity with respect to put option strikes and to the stochastic dominance constraints. Finally, we demonstrate the effect of the scenario tree contamination.
Investment Management and Financial Innovations
The asset management sector is constantly looking for a reliable investment strategy, which is ab... more The asset management sector is constantly looking for a reliable investment strategy, which is able to keep its promises. One of the most used approaches is the target volatility strategy that combines a risky asset with a risk-free trying to maintain the portfolio volatility constant over time. Several analyses highlight that such target is fulfilled on average, but in periods of crisis, the portfolio still suffers market’s turmoils. In this paper, the authors introduce an innovative target volatility strategy: the discontinuous target volatility. Such approach turns out to be more conservative in high volatility periods. Moreover, the authors compare the adoption of the VIX Index as a risk measure instead of the classical standard deviation and show whether the former is better than the latter. In the last section, the authors also extend the analysis to remove the risk-free assumption and to include the correlation structure between two risky assets. Empirical results on a wide t...
IMA Journal of Management Mathematics, 2016
Handbook of Asset and Liability Management, 2006
International Journal of Financial Engineering and Risk Management, 2015
The aim of this paper is to analyse the pricing of highly structured convertible bonds by taking ... more The aim of this paper is to analyse the pricing of highly structured convertible bonds by taking a real world case. To this end we examine the Cashes (Convertible And Subordinated Hybrid Equity-linked Securities), which are characterized by both voluntary and mandatory conversion that depend on different triggering events, as well as floating coupons whose payment hinges on dividends and earning of the issuer. Our results highlight that prices are very sensitive to the modelling of the sources of uncertainty, both market and credit risk, and underscore the relevance of the time horizon chosen for the estimation.
Computational Management Science
Multistage stochastic optimization is used to solve many real-life problems where decisions are t... more Multistage stochastic optimization is used to solve many real-life problems where decisions are taken at multiple times. Such problems need the representation of stochastic processes, which are usually approximated by scenario trees. In this article, we implement seven scenario reduction algorithms: three based on random extraction, named Random, and four based on specific distance measures, named Distance-based. Three of the latter are well known in literature while the fourth is a new approach, namely nodal clustering. We compare all the algorithms in terms of computational cost and information cost. The computational cost is measured by the time needed for the reduction, while the information cost is measured by the nested distance between the original and the reduced tree. Moreover, we also formulate and solve a multistage stochastic portfolio selection problem to measure the distance between the optimal solutions and between the optimal objective values of the original and the ...
Journal of Financial Management, Markets and Institutions
Investment certificates are securitized derivatives built as a combination of financial instrumen... more Investment certificates are securitized derivatives built as a combination of financial instruments. The financial engineering process aims to create new payoff profiles that allow investors to diversify or to hedge the risk of their portfolios. Such instruments are relatively challenging to price, as highlighted in the recent publications for other European markets. The aim of this paper is to analyze whether in the Italian market there are also differences between the quoted price and the estimated price obtained applying a standard pricing approach well known in the literature. In particular, we analyze three representative certificates, belonging to the classes of target coupon certificates and autocallable certificates, that have been most appreciated by the investors during the last years. To evaluate the price, we propose a Monte Carlo approach that computes directly the payoff of the certificates on a set of scenarios for the evolution of the underlying asset. Moreover, stud...
Annals of Operations Research
Frontiers in Finance and Economics, 2007
Standard methodologies for the derivation of implied trees from option prices are based on the va... more Standard methodologies for the derivation of implied trees from option prices are based on the validity of the put-call parity. Muzzioli and Torricelli (2002) propose a methodology which accounts for PCP violations. Based on this latter approach the present paper advances in two main directions. First we propose a different methodology in order to imply the interval of artificial probabilities at each node of the tree. Secondly, we perform an empirical validation of the implied tree obtained, both in the sample and out of sample, by using DAX index options data set covering the period from January 4, 1999 to December 28, 2000. Numerical results are compared with one of the most used standard methodologies, i.e. Derman and Kani's. The results suggest that the estimation proposed, by taking into account the informational content of both call and put prices, highly improves both the in-the-sample fitting and the out-of-sample performance.
Postoptimality for Scenario Based Financial Planning Models with an Application to Bond Portfolio... more Postoptimality for Scenario Based Financial Planning Models with an Application to Bond Portfolio Management Jitka Dupacovd, Marida Bertocchi and Vittorio Mori99ia Abstract The contamination technique is presented as a numerically tractable tech-nique for postoptimality analysis ...
Abstract Stochastic programming is a tool to support bond portfolio management decisions. For a s... more Abstract Stochastic programming is a tool to support bond portfolio management decisions. For a successful application of the stochastic programming methodology, one must choose an adequate model, asses its parameters, generate sensible input scenarios or scenario ...
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Papers by Vittorio Moriggia