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ON THE RUIN PROBLEM WITH INVESTMENT WHEN THE RISKY ASSET IS A SEMIMARTINGALE
- Publication Year :
- 2019
- Publisher :
- HAL CCSD, 2019.
-
Abstract
- In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\'e}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases. When R is a L{\'e}vy process, we retrieve the well-known results. Then, we show that these bounds are asymptotically optimal in the finite time case, under some simple conditions on the characteristics of X. Finally, we obtain a condition for ruin with probability one when X is a Brownian motion with negative drift and express it explicitly using the characteristics of R.
- Subjects :
- Statistics and Probability
[QFIN.RM]Quantitative Finance [q-fin]/Risk Management [q-fin.RM]
01 natural sciences
Lévy process
[QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP]
010104 statistics & probability
Quantitative Finance - Computational Finance
Mathematics::Probability
Simple (abstract algebra)
semimartingales
Return on investment
Applied mathematics
ruin probability
0101 mathematics
Power function
Brownian motion
Mathematics
010102 general mathematics
Investment (macroeconomics)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Asymptotically optimal algorithm
Semimartingale
Lévy processes
Statistics, Probability and Uncertainty
Mathematics - Probability
Quantitative Finance - Risk Management
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....e9823dc3a8c4ee1a9937cc90a75178dd