Time-consistent conditional expectation under probability distortion
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time-inconsistency, that is, the usual "tower property" fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step towards a new understanding of nonlinear expectations under probability distortion, and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.
Code (0)
등록된 구현이 없습니다.
Tasks
Stochastic OptimizationvalidSimilar Papers 제목 키워드 기반
Avoiding zero probability events when computing Value at Risk contributions
This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). We recast the traditional Euler contributions from an expectation c…
On the Correspondence and the Risk Contribution for Conditional Coherent and Deviation Risk Measures
We give an axiomatic framework for conditional generalized deviation measures. Under financially reasonable assumptions, we give the correspondence between conditional coherent risk measures and generalized deviation mea…
A conditional version of the second fundamental theorem of asset pricing in discrete time
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitr…
PIT-SUN: A Deployable Empirical Marginal Transform Framework with Expectation-Consistent Recovery for Regression in Recommender Systems
Estimating original-space conditional expectations is central to value-driven recommender systems, including dwell time, GMV, and LTV forecasting. Standard MSE is expectation-consistent in principle, but its gradients be…
Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
Conditional expectation operators (CEOs) and their associated conditional mean embeddings (CMEs) play a central role across applied mathematics and machine learning, appearing in nonparametric regression, Bayesian invers…