Worst case model risk management

Denis Talay () and Ziyu Zheng
Additional contact information
Denis Talay: INRIA, 2004 route des Lucioles, BP 93, 06902 Sophia Antipolis cedex, France Manuscript

Finance and Stochastics, 2002, vol. 6, issue 4, 517-537

Abstract: We are interested in model risk control problems. We study a strategy for the trader which, in a sense, guarantees good performances whatever is the unknown model for the assets of his/her portfolio. The trader chooses trading strategies to decrease the risk and therefore acts as a minimizer; the market systematically acts against the interest of the trader, so that we consider it acts as a maximizer. Thus we consider the model risk control problem as a two players (Trader versus Market) zero-sum stochastic differential game problem. Therefore our construction corresponds to a `worst case' worry and, in this sense, can be viewed as a continuous-time extension of discrete-time strategies based upon prescriptions issued from VaR analyses at the beginning of each period. In addition, the initial value of the optimal portfolio can be seen as the minimal amount of money which is needed to face the worst possible damage. We give a proper mathematical statement for such a game problem. We prove that the value function of this game problem is the unique viscosity solution to an Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation, and satisfies the Dynamic Programming Principle.

Keywords: Model risk; stochastic differential game; Hamilton-Jacobi-Bellman-Isaacs equation (search for similar items in EconPapers)
JEL-codes: G11 (search for similar items in EconPapers)
Date: 2002-08-19
Note: received: November 2000; final version received: February 2002
References: Add references at CitEc
Citations: View citations in EconPapers (37)

Downloads: (external link)
http://link.springer.de/link/service/journals/00780/papers/2006004/20060517.pdf (application/pdf)
Access to the full text of the articles in this series is restricted

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:6:y:2002:i:4:p:517-537

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().