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A BSDE with default jump and unbounded terminal value arising in a Principal-Agent context

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  • Jessica Martin

    (INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse)

Abstract

Analysis of some problems from the field of Economics, called Principal-Agent problems, can lead to the derivation of a Backward Stochastic Differential Equation (BSDE) for which existence and uniqueness of solutions is required. In this paper, we tackle such an object in a setting where both a Brownian motion and default process co-exist. This BSDE is crucial for the analysis of Principal-Agent problems under a risk of economic shutdown as done in the companion paper [16] and the main departure from existing literature on similar equations such as [12] is an unbounded terminal condition. In order to deal with existence, we use a result from [14] to reduce the problem to proving existence of solutions to a solely Brownian BSDE for which we adapt the method of Briand and Hu from [2] using a key result from [12]. Uniqueness is then obtained through martingale properties of the process.

Suggested Citation

  • Jessica Martin, 2021. "A BSDE with default jump and unbounded terminal value arising in a Principal-Agent context," Working Papers hal-03106006, HAL.
    • Handle: RePEc:hal:wpaper:hal-03106006
    Note: View the original document on HAL open archive server: https://hal.science/hal-03106006
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    References listed on IDEAS

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    1. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
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    Cited by:

    1. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Post-Print hal-04164688, HAL.

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