English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the problem of utility maximization with exponential preferencesin a market where the traded stock/risky asset price is modelled as aL\'evy-driven pure jump process (i.e. the driving L\'evy process has noBrownian component). In this setting, we study the terminal utilityoptimization problem in the presence of a European contingent claim. Weconsider in detail the BSDE (backward stochastic differential equation)characterising the value function when using an exponential utility function.First we analyse the well-definedness of the generator. This leads to someconditions on the market model related to conditions for the market to admit nofree lunches. Then we give bounds on the candidate optimal strategy.  Thereafter, we discuss the example of a cross-hedging problem and, undersevere assumptions on the structure of the claim, we give explicit solutions.Finally, we establish an explicit solution for a related BSDE with a suitableterminal condition but a simpler generator.

A BSDE arising in an exponential utility maximization problem in a pure jump market model