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Risk-minimizing pricing and Esscher transform in a general non-Markovian regime-switching jump-diffusion model

  • * Corresponding author

    * Corresponding author 
Tak Kuen Siu would like to acknowledge a Discovery Grant from the Australian Research Council (ARC), (Project No.: DP130103517). Yang Shen would like to acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), (Project No.: RGPIN-2016-05677).
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  • 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].

    Mathematics Subject Classification: Primary:58F15, 58F17;Secondary:53C35.


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