Optimization problem and mean variance hedging on defaultable claims

2012/09/26 by Stephane Goutte, Goutte, Stephane, Armand Ngoupeyou +1
Economics, Econometrics and Finance · Mathematics · #49L20 #60G48 #60H10 #91G40 #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #math.OC #math.PR #msc:49L20 #msc:60G48 #msc:60H10 #msc:91G40 #q-fin.PR

paper · pdf · doi:10.48550/arxiv.1209.5953

34 pages

arxiv created 2012/09/26 · arxiv updated 2012/09/27

Abstract

We study the pricing and the hedging of claim ψ which depends on the default times of two firms A and B. In fact, we assume that, in the market, we can not buy or sell any defaultable bond of the firm B but we can only trade defaultable bond of the firm A. Our aim is then to find the best price and hedging of ψ using only bond of the firm A. Hence, we solve this problem in two cases: firstly in a Markov framework using indifference price and solving a system of Hamilton-Jacobi-Bellman equations, secondly, in a more general framework, using the mean variance hedging approach and solving backward stochastic differential equations (BSDE).

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