共查询到3条相似文献,搜索用时 0 毫秒
1.
Peter Løchte Jørgensen 《Scandinavian actuarial journal》2016,2016(9):837-857
This paper provides the explicit solution to the three-factor diffusion model recently proposed by the Danish Society of Actuaries to the Danish industry of life insurance and pensions. The solution is obtained by use of the known general solution to multidimensional linear stochastic differential equation systems. With offset in the explicit solution, we establish the conditional distribution of the future state variables which allows for exact simulation. Using exact simulation, we illustrate how simulation of the system can be improved compared to a standard Euler scheme. In order to analyze the effect of choosing the exact simulation scheme over the traditional Euler approximation scheme frequently applied by practitioners, we carry out a simulation study. We show that due to its recursive nature, the Euler scheme becomes computationally expensive as it requires a small step size in order to minimize discretization errors. Using our exact simulation scheme, one is able to cut these computational costs significantly and obtain even better forecasts. As probability density tail behavior is key to expected investment portfolio performance, we further conduct a risk analysis in which we compare well-known risk measures under both schemes. Finally, we conduct a sensitivity analysis and find that the relative performance of the two schemes depends on the chosen model parameter estimates. 相似文献
2.
In Joon Kim In-Seok Baek Jaesun Noh Sol Kim 《Review of Quantitative Finance and Accounting》2007,29(1):69-110
This paper investigates the role of stochastic volatility and return jumps in reproducing the volatility dynamics and the
shape characteristics of the Korean Composite Stock Price Index (KOSPI) 200 returns distribution. Using efficient method of
moments and reprojection analysis, we find that stochastic volatility models, both with and without return jumps, capture
return dynamics surprisingly well. The stochastic volatility model without return jumps, however, cannot fully reproduce the
conditional kurtosis implied by the data. Return jumps successfully complement this gap. We also find that return jumps are
essential in capturing the volatility smirk effects observed in short-term options.
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Sol KimEmail: |
3.
According to Solvency II directive, each insurance company could determine solvency capital requirements using its own, tailor made, internal model. This highlights the urgency of having fast numerical tools based on practically-oriented mathematical models. From the Solvency II perspective discrete time framework seems to be the most relevant one. In this paper, we propose a number of fast and accurate approximations of ruin probabilities involving some integral operator and examine them along strictly theoretical as well as numerical lines. For a few claim distributions the approximations are shown to be exact. In general, we prove that they converge with an exponential rate to the exact ruin probabilities without any restrictive assumptions on the claim distribution. A fast algorithm to approximate ruin probabilities by a numerical fixed point of the involved integral operator is given. As an application, ruin probabilities for, e.g. normally and Weibull – distributed claims are computed. Comparisons with discrete time counterparts of some continuous time approximation methods are also carried out. Numerical studies show that our approximations are precise both for small and large values of the initial surplus u. In contrast, the empirical De Vylder-type ones strongly depend on the claim distributions and are less precise for small and medium values of u. 相似文献