Seminario del 2025

Febbraio
19
2025
Claudia Ceci
Optimal Self-Protection via BSDEs for risk models with jump clusters
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
finanza matematica
probabilità
We investigate the optimal self-protection problem, from the point of view of an insurance buyer, when the loss process is described by a Cox-shot-noise process and a Hawkes process with an exponential memory kernel. The insurance buyer chooses both the percentage of insured losses and the prevention effort. The latter term refers to actions aimed at reducing the frequency of the claim arrivals. The problem consists in maximizing the expected exponential utility of terminal wealth, in presence of a terminal reimbursement. We show that this problem can be formulated in terms of a suitable backward stochastic differential equation (BSDE), for which we prove existence and uniqueness of the solution. We extend in several directions the results obtained by Bensalem, Santibanez and Kazi-Tani [Finance Stoch. 2023] and compare our results with those presented therein. The talk is based on a joint paper with M. Brachetta, G. Callegaro and C. Sgarra.
organizzato da: Elena Bandini
nell'ambito del Progetto P.R.I.N. PRIN2022_PASCUCCI CUP J53D23003800006 del prof. Andrea Pascucci

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