## Journal of Applied Probability

- J. Appl. Probab.
- Volume 49, Number 4 (2012), 954-966.

### Ruin probabilities in a finite-horizon risk model with investment and reinsurance

#### Abstract

A finite-horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Our setting is innovative in the sense that we describe in a unified way the timing of the events, that is, the arrivals of claims and the changes of the prices in the financial market, by means of a continuous-time semi-Markov process which appears to be more realistic than, say, classical diffusion-based models. Obtaining explicit optimal solutions for the minimizing ruin probability is a difficult task. Therefore we derive a specific methodology, based on recursive relations for the ruin probability, to obtain a reinsurance and investment policy that minimizes an exponential bound (Lundberg-type bound) on the ruin probability.

#### Article information

**Source**

J. Appl. Probab., Volume 49, Number 4 (2012), 954-966.

**Dates**

First available in Project Euclid: 5 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1354716650

**Digital Object Identifier**

doi:10.1239/jap/1354716650

**Mathematical Reviews number (MathSciNet)**

MR3058981

**Zentralblatt MATH identifier**

1255.91185

**Subjects**

Primary: 91B30: Risk theory, insurance 93E20: Optimal stochastic control 60J28: Applications of continuous-time Markov processes on discrete state spaces

**Keywords**

Risk process semi-Markov process optimal reinsurance and investment Lundberg-type bound

#### Citation

Romera, R.; Runggaldier, W. Ruin probabilities in a finite-horizon risk model with investment and reinsurance. J. Appl. Probab. 49 (2012), no. 4, 954--966. doi:10.1239/jap/1354716650. https://projecteuclid.org/euclid.jap/1354716650