Stochastic ordering by g-expectations

2020/05/26 by Sel Ly, Ly, Sel, Nicolas Privault +1 · 1 citation
Economics, Econometrics and Finance · Social Sciences · #35B51 #60E15 #60H10 #60H30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2005.12580

openalex publication_date 2020/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity, monotonicity and continuous dependence properties for the solutions of associated semilinear parabolic partial differential equations. Applications to contingent claim price comparison under different hedging portfolio constraints are provided.

Citations

• Conjugate convex functions in optimal stochastic control

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