Exponential utility optimization, indifference pricing and hedging for a payment process

Volume 39 / 2012

Łukasz Delong Applicationes Mathematicae 39 (2012), 211-229 MSC: 91B16, 91B30, 93E20. DOI: 10.4064/am39-2-7

Abstract

We deal with pricing and hedging for a payment process. We investigate a Black–Scholes financial market with stochastic coefficients and a stream of liabilities with claims occurring at random times, continuously over the duration of the contract and at the terminal time. The random times of the claims are generated by a random measure with a stochastic intensity of jumps. The claims are written on the asset traded in the financial market and on the non-tradeable source of risk driven by the random measure. Our framework allows us to consider very general streams of liabilities which may arise in financial and insurance applications. We solve the exponential utility optimization problem for our payment process and we derive the indifference price and hedging strategy. We apply backward stochastic differential equations.

Authors

  • Łukasz DelongInstitute of Econometrics, Division of Probabilistic Methods
    Warsaw School of Economics
    Al. Niepodległości 162
    02-554 Warszawa, Poland
    e-mail

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