Work

Downside risk minimization via a large deviations approach

Year: 2012

Type: article

Abstract: We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model, and then study the asymptotic behavior of minimizing probability as T → ∞. This problem can be closely related to an ergodic risk-sensitive stochastic control problem in the risk-averse case. Indeed, in our main theorem, we relate the former problem concerning the asymptotics for risk minimization to the latter as its dual. As a result, we obtain an expression of the limit value of the probability as the Legendre transform of the value of the control problem, which is characterized as the solution to an H-J-B equation of ergodic type, in the case of a Markovian incomplete market model.

Source: The Annals of Applied Probability

DOI: 10.1214/11-aap781

Author: Hideo Nagai

Institution: The University of Osaka

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: Japan Society for the Promotion of Science

Awards: Development of the methods of stochastic control and filtering in mathematical finance, Numerical Analysis of Jump-Models and Applications of Malliavin Calculus in Finance, Deepening of the theory of viscosity solutions and its applications