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

Łukasz Delong¹

¹ Institute of Econometrics, Division of Probabilistic Methods Warsaw School of Economics Al. Niepodległości 162 02-554 Warszawa, Poland

Applicationes Mathematicae, Tome 39 (2012) no. 2, pp. 211-229

Résumé

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.

Détail

DOI : 10.4064/am39-2-7

Keywords: pricing hedging payment process investigate black scholes financial market stochastic coefficients stream liabilities claims occurring random times continuously duration contract terminal time random times claims generated random measure stochastic intensity jumps claims written asset traded financial market non tradeable source risk driven random measure framework allows consider general streams liabilities which may arise financial insurance applications solve exponential utility optimization problem payment process derive indifference price hedging strategy apply backward stochastic differential equations