A note on r-balayages of matrix-exponential L'evy processes

Yuan-Chung Sheu (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)
Yu-Ting Chen (Institute of Mathematics, Academia Sinica, Taipei, Taiwan)

Abstract


In this note we give semi-explicit solutions for $r$-balayages of matrix-exponential-Lévy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative Wiener-Hopf factor. Our result is closely related to the works by Mordecki in [11], Asmussen, Avram and Pistorius in [3], Chen, Lee and Sheu in [7], and many others

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Pages: 165-175

Publication Date: April 21, 2009

DOI: 10.1214/ECP.v14-1456

References

  1. Alili, L., Kyprianou, A.E. Some remarks on first passage of LÈvy processes, the American put and pasting principles. Annals of Applied Probability 15 (2005), 2062-2080. MR2152253 (2006b:60078).
  2. Asmussen, S. Applied Probability and Queues, Vol.51 of Applications of Mathematics (New York). 2nd edition, Springer-Verlag, Berlin, (2003). MR1978607 (2004f:60001).
  3. Asmussen, S., Avram, F., Pistorius, M.R. Russian and American put options under exponential phase-type LÈvy modesl. Stochastic Processes and Their Applications 109 (2004), 79-111. MR2024845 (2004m:91096).
  4. Avram, F., Usabel, M. Finite time ruin probabilities with one Laplace transform. Insurance, Mathematics and Economics 32 (2003), 371-377. MR1994498.
  5. Botta, R.F., Harris, C.M. Approximation with generalized hyperexponential distributions: weak convergence results. Queueing Systems 2 (1986), 169-190. MR0896234 (88i:60145)
  6. Boyarchenko, S., Levendorskii, S. American options: the EPV pricing model. Annals of Finance 1 (2005), 267-292. Math. Review number not available.
  7. Chen, Y.T., Lee, C.F., Sheu, Y.C. An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model. Finance and Stochastics 11 (2007), 323-355. MR2322916 (2008h:91085)
  8. Dixit, A.K., Pyndick, R.S. Investment under Uncertainty. Princeton University Press, New Jersey, (1994). Math. Review number not available.
  9. Gerber, H.U., Shiu, E.S.W. On the time value of ruin. North American Actuarial Journal 2 (1998), 48-78. MR1988433
  10. Lewis, A.L., Mordecki, E. Wiener-Hopf factorization for LÈvy processes having positive jumps with rational transforms. Journal of Applied Probability 45 (2008), 118-134. MR2409315 (2009d:60144)
  11. Mordecki, E. Optimal stopping and perpetual options for LÈvy processes. Finance and Stochastics 6 (2002), 473-493. MR1932381 (2003j:91059)
  12. Sato, K. LÈvy processes and infinitely divisible distributions. Cambridge University Press, Cambridge, (1999). MR1739520 (2003b:60064)
  13. Stein, E.M., Shakarchi, R. Real Analysis, Princeton Lectures in Analysis III. Princeton University Press, New Jersey,(2005). MR2129625 (2005k:28024)
  14. Stein, E.M., Shakarchi, R. Fourier Analysis, Princeton Lectures in Analysis I. Princeton University Press, New Jersey, (2003). MR1970295 (2004a:42001)
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