TY - JOUR
T1 - Sub-optimal investment for insurers
AU - Longo, Michele
AU - Stabile, Gabriele
PY - 2019
Y1 - 2019
N2 - We consider the investment problem for a non-life insurance company seeking to minimize the ruin probability. Its reserve is described by a perturbed risk process possibly correlated with the financial market. Assuming exponential claim size, the Hamilton-Jacobi-Bellman equation reduces to a first order nonlinear ordinary differential equation, which seems hard to solve explicitly. We study the qualitative behavior of its solution and determine the Cramer-Lundberg approximation. Moreover, our approach enables to find very naturally that the optimal investment strategy is not constant. Then, we analyze how much the company looses by adopting sub-optimal constant (amount) investment strategies.
AB - We consider the investment problem for a non-life insurance company seeking to minimize the ruin probability. Its reserve is described by a perturbed risk process possibly correlated with the financial market. Assuming exponential claim size, the Hamilton-Jacobi-Bellman equation reduces to a first order nonlinear ordinary differential equation, which seems hard to solve explicitly. We study the qualitative behavior of its solution and determine the Cramer-Lundberg approximation. Moreover, our approach enables to find very naturally that the optimal investment strategy is not constant. Then, we analyze how much the company looses by adopting sub-optimal constant (amount) investment strategies.
KW - Insurance risk process
KW - Investment
KW - Ruin probability
KW - Sub-optimal strategies
KW - Insurance risk process
KW - Investment
KW - Ruin probability
KW - Sub-optimal strategies
UR - https://publicatt.unicatt.it/handle/10807/134300
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85064761241&origin=inward
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85064761241&origin=inward
U2 - 10.1080/03610926.2019.1599020
DO - 10.1080/03610926.2019.1599020
M3 - Article
SN - 0361-0926
VL - 49
SP - 4298
EP - 4312
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 17
ER -