## Journal of Applied Probability

- J. Appl. Probab.
- Volume 50, Number 2 (2013), 309-322.

### On joint ruin probabilities of a two-dimensional risk model with constant interest rate

#### Abstract

In this note we consider the two-dimensional risk model introduced in
Avram, Palmowski and Pistorius (2008) with constant interest rate. We
derive the integral-differential equations of the Laplace transforms, and
asymptotic expressions for the finite-time ruin probabilities with respect
to the joint ruin times *T*_{max}(*u*_{1},*u*_{2}) and *T*_{min}(*u*_{1},*u*_{2})
respectively.

#### Article information

**Source**

J. Appl. Probab., Volume 50, Number 2 (2013), 309-322.

**Dates**

First available in Project Euclid: 19 June 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1371648943

**Digital Object Identifier**

doi:10.1239/jap/1371648943

**Mathematical Reviews number (MathSciNet)**

MR3102482

**Zentralblatt MATH identifier**

1266.91034

**Subjects**

Primary: 91B30: Risk theory, insurance

Secondary: 60J25: Continuous-time Markov processes on general state spaces

**Keywords**

Two-dimensional risk model constant interest rate joint ruin probability integral-differential equation asymptotic expression

#### Citation

Hu, Zechun; Jiang, Bin. On joint ruin probabilities of a two-dimensional risk model with constant interest rate. J. Appl. Probab. 50 (2013), no. 2, 309--322. doi:10.1239/jap/1371648943. https://projecteuclid.org/euclid.jap/1371648943