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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study an optimal investment problem under contagion risk in a financialmodel subject to multiple jumps and defaults. The global market information isformulated as a progressive enlargement of a default-free Brownian filtration,and the dependence of default times is modeled by a conditional densityhypothesis. In this Ito-jump process model, we give a decomposition of thecorresponding stochastic control problem into stochastic control problems inthe default-free filtration, which are determined in a backward induction. Thedynamic programming method leads to a backward recursive system of quadraticbackward stochastic differential equations (BSDEs) in Brownian filtration, andour main result proves, under fairly general conditions, the existence anduniqueness of a solution to this system, which characterizes explicitly thevalue function and optimal strategies to the optimal investment problem. Weillustrate our solutions approach with some numerical tests emphasizing theimpact of default intensities, loss or gain at defaults and correlation betweenassets. Beyond the financial problem, our decomposition approach provides a newperspective for solving quadratic BSDEs with a finite number of jumps.

Optimal investment under multiple defaults risk: A BSDE-decomposition approach