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A comparison result for FBSDE with applications to decisions theory

Author

Listed:
  • Fabio Antonelli
  • Emilio Barucci
  • Maria Elvira Mancino

Abstract

In general, a comparison Lemma for the solutions of Forward-Backward Stochastic Differential Equations (FBSDE) does not hold. Here we prove one for the backward component at the initial time, relying on certain monotonicity conditions on the coefficients of both components. Such a result is useful in applications. Indeed, one can use FBSDE's to define a utility functional able to capture the disappointment-anticipation effect for an agent in an intertemporal setting under risk. Exploiting our comparison result, we prove some “desirable” properties for the utility functional, such as continuity, concavity, monotonicity and risk aversion. Finally, for completeness, in a Markovian setting, we characterize the utility process by means of a degenerate parabolic partial differential equation. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Fabio Antonelli & Emilio Barucci & Maria Elvira Mancino, 2001. "A comparison result for FBSDE with applications to decisions theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 407-423, December.
    • Handle: RePEc:spr:mathme:v:54:y:2001:i:3:p:407-423
    DOI: 10.1007/s001860100165
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    Keywords

    Key words: Forward-Backward SDE's; Comparison Theorem; Utility; Habit; Classification: (AMS 2000) 60H; 90A10; (JEL 1999) C61; D11; D81;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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