Machine learning in individual claims reserving

Machine learning techniques make it feasible to calculate claims reserves on individual claims data. This paper illustrates how these techniques can be used by providing an explicit example in individual claims reserving.     

Automatic balancing mechanisms for notional defined contribution accounts in the presence of uncertainty

The notional defined contribution model combines pay-as-you-go financing and a defined contribution pension formula. This paper aims to demonstrate the extent to which liquidity and solvency indicators are affected by fluctuations in economic and demographic conditions and to explore the introduction of an automatic balancing mechanism (ABM) into the pension scheme. We demonstrate that the introduction of an ABM reduces the volatility of the buffer fund and that, in most cases, the automatic mechanism that re-establishes solvency produces the highest value of the risk-adjusted notional factor.     

Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy.     

保险公司市场风险经济资本度量研究

经济资本(EC)是在既定期间和置信水平下,公司根据实际承担的风险计算的用以吸收非预期损失的资本额度,目前市场风险是整体经济资本测算体系中最为突出的风险.根据当前保险运营与资产投资的比例特征,同时对资产端与负债端建立市场风险投资模型,采用嵌套随机模拟方法进行两阶段情景生成,度量未来一年内不同风险测度下的市场风险经济资本需求,并对比不同情景数量下的测算稳定性.结果证明:随着内部或外部情景模拟次数的增加,市场风险经济资本测算结果对于极端风险的预测趋于稳定,在内外部情景数量乘积相同时运算时间基本一致.当内外部两阶段情景生成参数差异较大的情形下,应适当增加情景生成数量,以确保对于极端风险预测的准确性.     

非封闭的SIS确定模型与随机模型的研究

文章通过对具常数输入人口,死亡率和出生率的的SIS模型的确定形式与随机形式的研究,得到文中定义的基本再生数R0燮1时,传染病最终会消失,而当基本再生数大于等1时,传染病人数将稳定,传染病最终会形成地方病,最后验证了两种模型的结果是一致的。     

森林资源资产组合随机控制模型及决策

在界定了森林生态资产与森林资源资产组合概念的基础上,构建和模拟了基于随机控制理论的森林资源资产组合模型,为森林经营管理者提出了相应的结论和建议:森林经营管理者可以根据最优采伐量与木材价格、补偿价格、成本系数、税率、贴现率、生长率等参数之间的关系,获得在市场经济变动条件下的最优森林资产组合,以保证森林资产净收益的稳定增长。     

PRICING DERIVATIVES ON MULTISCALE DIFFUSIONS: AN EIGENFUNCTION EXPANSION APPROACH

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a large class of derivative‐assets. The payoff of the derivative‐assets may be path‐dependent. In addition, the process underlying the derivatives may exhibit killing (i.e., jump to default) as well as combined local/nonlocal stochastic volatility. The nonlocal component of volatility may be multiscale, in the sense that it may be driven by one fast‐varying and one slow‐varying factor. The flexibility of our modeling framework is contrasted by the simplicity of our method. We reduce the derivative pricing problem to that of solving a single eigenvalue equation. Once the eigenvalue equation is solved, the approximate price of a derivative can be calculated formulaically. To illustrate our method, we calculate the approximate price of three derivative‐assets: a vanilla option on a defaultable stock, a path‐dependent option on a nondefaultable stock, and a bond in a short‐rate model.     

Intra-market sovereign linkages of key Latin American markets

This paper tests the intra-market dynamics in a regional setting using country-specific international bonds differentiated only by maturity within individual markets in the Latin American region. We use the 2001 Argentine default as a natural experiment in this study to examine how intra-market dynamics evolved in the presence of a credit event in the region. This paper argues that emerging market instruments have a stronger tendency to tie up with instruments within markets rather than across markets as found in the literature. The long-run equilibrium relationships tend to be stronger across instruments within each market and generate economically insignificant portfolio adjustment weights. Strong interaction across instruments within markets in terms of first order dependencies has important implications for market participants, practitioners and policymakers.     

Optimal constrained investment in the Cramer-Lundberg model

We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk-free asset and in a risky asset, governed by the Black-Scholes equation. There is a constraint that the insurance company can only invest in the risky asset at a limited leveraging level; more precisely, when purchasing, the ratio of the investment amount in the risky asset to the surplus level is no more than a; and when short-selling, the proportion of the proceeds from the short-selling to the surplus level is no more than b. The objective is to find an optimal investment policy that minimizes the probability of ruin. The minimal ruin probability as a function of the initial surplus is characterized by a classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We study the optimal control policy and its properties. The interrelation between the parameters of the model plays a crucial role in the qualitative behavior of the optimal policy. For example, for some ratios between a and b, quite unusual and at first ostensibly counterintuitive policies may appear, like short-selling a stock with a higher rate of return to earn lower interest, or borrowing at a higher rate to invest in a stock with lower rate of return. This is in sharp contrast with the unrestricted case, first studied in Hipp and Plum, or with the case of no short-selling and no borrowing studied in Azcue and Muler.     

CLOSED FORM PRICING FORMULAS FOR DISCRETELY SAMPLED GENERALIZED VARIANCE SWAPS

Most of the existing pricing models of variance derivative products assume continuous sampling of the realized variance processes, though actual contractual specifications compute the realized variance based on sampling at discrete times. We present a general analytic approach for pricing discretely sampled generalized variance swaps under the stochastic volatility models with simultaneous jumps in the asset price and variance processes. The resulting pricing formula of the gamma swap is in closed form while those of the corridor variance swaps and conditional variance swaps take the form of one‐dimensional Fourier integrals. We also verify through analytic calculations the convergence of the asymptotic limit of the pricing formulas of the discretely sampled generalized variance swaps under vanishing sampling interval to the analytic pricing formulas of the continuously sampled counterparts. The proposed methodology can be applied to any affine model and other higher moments swaps as well. We examine the exposure to convexity (volatility of variance) and skew (correlation between the equity returns and variance process) of these discretely sampled generalized variance swaps. We explore the impact on the fair strike prices of these exotic variance swaps with respect to different sets of parameter values, like varying sampling frequencies, jump intensity, and width of the monitoring corridor.