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

Tak Kuen Siu*, Yang Shen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

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].

Original languageEnglish
Pages (from-to)2595-2626
Number of pages32
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume22
Issue number7
DOIs
Publication statusPublished - 1 Sep 2017

Keywords

  • Backward stochastic differential equations
  • Convex risk measures
  • Esscher transforms
  • Game theory
  • Non-Markovian regime-switching jump diffusion
  • Option valuation

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