Optimal Stopping for Dynamic Convex Risk Measures

By Erhan Bayraktar, Ioannis Karatzas, Song Yao. 2009

71 citations recorded by the source corpus.

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the “stopper”) who chooses the termination time of the game, and an agent (the “controller”, or “nature”) who selects the probability measure.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/caaeaa36d4b163f9bd35121dd30a4cecff1ccd58

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Marcel Nutz
2. Jianfeng Zhang
3. Peter Imkeller
4. Miryana Grigorova
5. Y. Ouknine
6. Marie Claire Quenez
7. Nizar Touzi
8. Agnès Sulem

In Finance

1. Marcel Nutz
2. Jianfeng Zhang
3. Nizar Touzi
4. Peter Imkeller
5. Ibrahim Ekren
6. Y. Ouknine
7. Miryana Grigorova
8. Marie Claire Quenez

In Management Science and Operations Research

1. Marcel Nutz
2. Jianfeng Zhang
3. Nizar Touzi
4. Peter Imkeller
5. Miryana Grigorova
6. Y. Ouknine
7. Ibrahim Ekren
8. Marie Claire Quenez

Citations in the corpus

• Reflected BSDEs when the obstacle is not right-continuous and optimal stopping (2015, methodology): “erators, the family of so-called f-conditional expectations, has been defined through the notion of BSDEs and used in the literature on dynamic risk measures (cf., for instance, [2], [32], [33], [35], [3] among others). MSC 2010 subject classifications: Primary 60G40, 93E20, 60H30; secondary 60G07, 47”
• Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps (2012, unknown): “n ε ′-optimal stopping time for the optimal stopping time problem (4.13) with ε′ = eβT2 ε. Note also that the above result does not require any concavity assumption on the driver, contrary to [1] and [2]. 4.2 Optimal stopping times We now provide an optimality criterium for the optimal stopping time”
• Optimal stopping under adverse nonlinear expectation and related games (2012, background): “For the case where P is dominated, the problem of optimal stopping under nonlinear expectation (and related risk measures) is fairly well studied; see, in particular, [3, 5, 6, 11, 13, 17, 18, 30].”
• Optimal stopping with f-expectations: The irregular case (2016, background): “As mentioned in the introduction, the above optimal stopping problem has been largely studied: in [13], and in [3], in the case of a continuous pay-o process ξ; in [36] and [1] in the case of a right-continuous pay-o ; and recently in [16] in the case of a right-uppersemicontinuous pay-o process ξ.”
• Optimal stopping under ambiguity in continuous time (2013, unknown): “[4] generalize to convex dynamic risk measures.”
• BSDEs with jumps, optimization and applications to dynamic risk measures (2013, background): “Many studies have been recently done on such dynamic risk measures, especially concerning relative robust optimization problems and optimal stopping problems (see, among others, Bayraktar and coauthors in [2]).”
• Optimal Stopping under Nonlinear Expectation (2012, background): “Consequently, the Snell envelope characterization of the optimal stopping problem under nonlinear expectation is available in the existing literature on reflected backward stochastic differential equations, see e.g. El Karoui et al [8], Bayraktar, Karatzas and Yao [1].”