Time-consistent and market-consistent evaluations
Mitja Stadje (Tilburg University, The Netherlands)
Joint work with Antoon Pelsser

Thursday June 5, 16:30-17:00 | session 9.3 | Risk Measures | room EF

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with a continuous stock prices process every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.

Rationality under Disappointment
Phillip Yam (The Chinese University of Hong Kong, Hong Kong)
Joint work with Ka Chun Cheung, Alfred Chong and Robert Elliott

Thursday June 5, 17:00-17:30 | session 9.3 | Risk Measures | room EF

As said by one of the most influential writers of the French Renaissance, Michel Eyquem de Montaigne, 'Disappointment and feebleness imprint upon us a cowardly and valetudinarian virtue'; however to what extent of this virtue? Is it rational? For decades, classical expected utility theory has constantly been challenged on its failure of capturing the real behavior of decision makers that, for example, results in Allais Paradox. To remedy its shortcoming, based on many experimental psychological observations, as one of the most representative theoretical models in behavioral finance, Disappointment Theory has been created (see Bell (1985) and Gul (1991)). In this talk, according to the usual economic concept of certainty equivalence, I shall introduce that the pricing principle, of a decision maker under Disappointment Theory, on any risky securities is a convex risk measure. Further properties of this special class of convex risk measures are illustrated. Explicit representations of the pricing principle are also established for common modeling examples. Our result here paves the first theoretical bridge between one of the most popular topics in behavioral finance and the rational theory of risk measures, which are used to be perceived as mutually exclusive in the literature.