2015/08/30 by Carla Mereu, Mereu, Carla, Robert Stelzer +1
Economics, Econometrics and Finance · #60H10 #60J75 #93E20 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Primary: 91G80 Secondary: 60G51 #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1508.07561
openalex publication_date 2015/08/30 · openalex created_date 2022/03/05 · openalex updated_date 2026/07/28
We consider the problem of utility maximization with exponential preferences\nin a market where the traded stock/risky asset price is modelled as a\nL 'evy-driven pure jump process (i.e. the driving L 'evy process has no\nBrownian component). In this setting, we study the terminal utility\noptimization problem in the presence of a European contingent claim. We\nconsider in detail the BSDE (backward stochastic differential equation)\ncharacterising the value function when using an exponential utility function.\nFirst we analyse the well-definedness of the generator. This leads to some\nconditions on the market model related to conditions for the market to admit no\nfree lunches. Then we give bounds on the candidate optimal strategy.\n Thereafter, we discuss the example of a cross-hedging problem and, under\nsevere assumptions on the structure of the claim, we give explicit solutions.\nFinally, we establish an explicit solution for a related BSDE with a suitable\nterminal condition but a simpler generator.\n