Papers by Romuald Hervé Momeya
Mathematical Methods of Operations Research, 2017
In this paper, we present an optimal control problem for stochastic differential games under Mark... more In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for nonzerosum stochastic differential games problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for nonzero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty and to find optimal investment of an insurance firm under model uncertainty.
In this paper, the option hedging problem for a Markov-modulated exponential Lévy model is examin... more In this paper, the option hedging problem for a Markov-modulated exponential Lévy model is examined. We employ the local risk-minimization approach to study optimal hedging strategies for Europeans derivatives under both full information and then partial information.
In this paper, we present an optimal control problem for stochastic differential games under Mark... more In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for non zero-sum stochastic differential game problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for non zero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty. We also apply the results to find optimal investment of an insurance firm under model uncertainty.
Asia-Pacific Financial Markets, 2011
This paper deals with the characterization problem of the minimal entropy martingale measure (MEM... more This paper deals with the characterization problem of the minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model. This model is characterized by the presence of a background process modulating the risky asset price movements between different regimes or market environments. This allows to stress the strong dependence of financial assets price with structural changes in the market conditions. Our main results are obtained from the key idea of working conditionally on the modulator-factor process. This reduces the problem to studying the simpler case of processes with independent increments. Our work generalizes some previous works in the literature dealing with either the exponential Lévy case or the exponential-additive case.
Stochastics, 2018
In this paper, we investigate the pricing problem of a Europeanstyle contingent claim under a Mar... more In this paper, we investigate the pricing problem of a Europeanstyle contingent claim under a Markov-modulated exponential Lévy model. One of the main feature of this model is the modulator factor which takes into account the empirical facts observed in asset prices dynamics such as the long-term (stochastic) variability and time inhomogeneities. Using the viscosity solutions framework, we show that the value of a European-style option is the unique viscosity solution of a system of coupled linear Partial Integro-Differential Equations when the payoff function satisfies a Lipschitz condition. Moreover, we propose a numerical scheme for approximating solution of this system and discuss its stability, consistency and convergence.
Methodology and Computing in Applied Probability, 2014
Regime-switching models (RSM) have been recently used in the literature as alternatives to the Bl... more Regime-switching models (RSM) have been recently used in the literature as alternatives to the Black-Scholes model. Several authors favor RSM as being more realistic since, by construction, they model exogenous macroeconomic cycles against which asset prices evolve. In the context of derivatives pricing, these models lead to incomplete markets and, therefore, to the existenceof multiple Equivalent Martingale Measures (EMM) that yield dierent pricing rules. A fair amount of literature (Bungton and Elliott (2002), Elliott et al. (2005)) focuses on conveniently choosing a family of EMM leading to closed-form formulas for option prices. These studies often make the assumption that the risk associated with the Markov chain is not priced. Recently, Siu and Yang (2009), proposed an EMM kernel that takes into account all risk components of a regime-switching Black-Scholes model. In this paper, we study two families of EMM and their corresponding implicit assumptions in a more general setting than in Siu and Yang (2009). That is, we study two families of EMM for a general Lévy regime-switching model that allow us to assess the inuence of jumps on the price of risk. We specialize this general framework to Regime-switching Jump-Diusion and Variance-Gamma models and carry out a comparative analysis of the resulting option price formulas with existing regime-switching models such as Naik (1993) and Boyle and Draviam (2007).
Local Risk-Minimization Under Markov-Modulated Exponential Lévy Model
International Journal of Theoretical and Applied Finance, 2015
In this paper, the option hedging problem for a Markov-modulated exponential Lévy model is examin... more In this paper, the option hedging problem for a Markov-modulated exponential Lévy model is examined. We use the local risk-minimization approach to study optimal hedging strategies for Europeans derivatives when the price of the underlying is given by a regime-switching Lévy model. We use a martingale representation theorem result to construct an explicit local risk minimizing strategy.
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Papers by Romuald Hervé Momeya