Risk-Sensitive Probability for Markov Chains

The probability distribution of a Markov chain is viewed as the information state of an additive optimization problem. This optimization problem is then generalized to a product form whose information state gives rise to a generalized notion of probability distributionfor Markov chains. The evolution and the asymptoticbehavior of this generalized or "risk-sensitive"probability distribution is studied in this paper and a conjecture isproposed regarding the asymptotic periodicity of risk-sensitive probability. The relation between a set of simultaneous non-linear equations and the set of periodic attractors is analyzed. <p

Risk-sensitive investment in a finite-factor model

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The approach of Klebaner and Lipster (2014) is used to prove the martingale property of the relevant density processes.Comment: 23 pages, 1 figur