PRESENT VALUE DISTRIBUTIONS WITH APPLICATIONS TO RUIN THEORY AND STOCHASTIC-EQUATIONS

We study the distribution of the stochastic integral integral(0)(infin ity) e(-Rt) dP(t) where P and R are independent Levy processes with a finite number of jumps on finite time intervals. The exact distributio n is obtained in many special cases, and we derive asymptotic properti es of the tails of the distributions in the general case. These result s are applied to give two new examples of exact solutions of the proba bility of eventual ruin of an insurance portfolio where return on inve stments are stochastic. Finally we use the results to give new example s of exact solutions of the stochastic equations Z =(d) AZ + B and Z = (d) A(Z + C) where Z and (A,B) (or (A, C)) are independent. (C) 1997 E lsevier Science B.V.