RT Journal Article
T1 A numerical method for the expected penalty–reward function in a Markov-modulated jump–diffusion process
A1 Diko, Peter
A1 Usabel Rodrigo, Miguel Arturo
AB A generalization of the Cramér–Lundberg risk model perturbed by a diffusion is proposed. Aggregateclaims of an insurer follow a compound Poisson process and premiums are collected at a constantrate with additional random fluctuation. The insurer is allowed to invest the surplus into a risky assetwith volatility dependent on the level of the investment, which permits the incorporation of rationalinvestment strategies as proposed by Berk and Green (2004). The return on investment is modulated by aMarkov process which generalizes previously studied settings for the evolution of the interest rate in time.The Gerber–Shiu expected penalty–reward function is studied in this context, including ruin probabilities(a first-passage problem) as a special case. The second order integro-differential system of equations thatcharacterizes the function of interest is obtained. As a closed-form solution does not exist, a numericalprocedure based on the Chebyshev polynomial approximation through a collocation method is proposed.Finally, some examples illustrating the procedure are presented
PB Elsevier
SN 0167-6687
YR 2011
FD 2011-07
LK https://hdl.handle.net/10016/12757
UL https://hdl.handle.net/10016/12757
LA eng
DS e-Archivo
RD 3 may. 2024