Mean-variance portfolio selection for a non-life insurance company |
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Authors: | Łukasz Delong Russell Gerrard |
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Institution: | (1) Institute of Econometrics, Division of Probabilistic Methods, Warsaw School of Economics, Niepodległości 162, 02-554 Warsaw, Poland;(2) Faculty of Actuarial Science and Insurance, Cass Business School, 106 Bunhill Row, London, EC1Y 8TZ, UK |
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Abstract: | We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity
is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market
consisting of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise.
We investigate two optimization problems. The first one is the classical mean-variance portfolio selection. In this case the
efficient frontier is derived. The second optimization problem, except the mean-variance terminal objective, includes also
a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target which is a random process.
In order to find optimal strategies we apply techniques from the stochastic control theory. |
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Keywords: | Lévy diffusion financial market Compound Cox claim process Hamilton– Jacobi– Bellman equation Feynman– Kac representation Efficient frontier |
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