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Risk-minimizing pricing and Esscher transform in a general non-Markovian regime-switching jump-diffusion model. (English) Zbl 1414.91389

Summary: A risk-minimizing approach to pricing contingent claims in a general non-Markovian, regime-switching, jump-diffusion model is discussed, where a convex risk measure is used to describe risk. The pricing problem is formulated as a two-person, zero-sum, stochastic differential game between the seller of a contingent claim and the market, where the latter may be interpreted as a “fictitious” player. A backward stochastic differential equation (BSDE) approach is applied to discuss the game problem. Attention is given to the entropic risk measure, which is a particular type of convex risk measures. In this situation, a pricing kernel selected by an equilibrium state of the game problem is related to the one selected by the Esscher transform, which was introduced to the option-pricing world in the seminal work by [38].

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91A15 Stochastic games, stochastic differential games
91A23 Differential games (aspects of game theory)
91A05 2-person games
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J75 Jump processes (MSC2010)
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