报告题目：Recursive Nonzero-sum Stochastic Differential Games

报告 人：穆蕊

报告摘要： This talk is concerned with recursive nonzero-sum stochastic differential games in Markovian framework where the utilities are given by solutions of related BSDEs. We show the existence of a Nash equilibrium point for the game when the drift of the state process is no longer bounded under the generalized Isaacs assumption. The main tool is the notion of BSDEs which, in our case, are multidimensional with continuous coefficients. The generator is of stochastic linear growth on the volatility process and stochastic monotonic on the value process.

报告题目：Distorted Mix Method for Constructing Copulas with Tail Dependence

报告 人：杨静平

报告摘要：We will introduce a method for constructing copula functions by combining the ideas of distortion and convex sum, named Distorted Mix Method. The method mixes different copulas with distorted margins to construct new copula functions, and it enables us to model the dependence structure of risks by handling central and tail parts separately. By applying the method we can modify the tail dependence of a given copula to any desired level measured by tail dependence function and tail dependence coefficients of marginal distributions. As an application, a tight bound for asymptotic Value-at-Risk of order statistics is obtained by using the method. An empirical study shows that copulas constructed by this method fit the empirical data of SPX 500 Index and FTSE 100 Index very well in both central and tail parts. It is a joint work with Lujun Li and K. C. Yuen.

报告题目：Risk, Uncertainty and Sublinear Expectation

报告 人：徐玉红

报告摘要： Mathematical, or a priori, type of probability practically never met with in business. Uncertainty must be taken in a sense radically distinct from the familiar notion of risk, from which it has never been properly separated. Kolmogorov proved his modern version of the LLN in his book, whose enormous influence effaced the notion of nonadditivity from mainstream probability. Mathematical finance makes a recent visibility peak of this otherwise underground trend. This talk will present the theory of Peng''''s sublinear expectation and applications to characterize "Uncertainty" or "Ambiguity" which is popular in finance and economics.

报告题目：On a generalization of the multivariate Archimedean copula

报告 人：谢杰华

报告摘要：In this paper, we combine that general idea presented by Marshall-Olkin distributions with a multivariate Archimedean copula. We construct a multivariate copula n>2 with two generators. The copula proposed in this paper is a generalization of multivariate Archimedean copula. We show that how to construct this copula and present its properties. The new proposed copula is a good extension to the multivariate Archimedean copula since it is more flexible and effective in building a model for practical application than Archimedean copula. Furthermore, we also give the results of the multivariate tail dependence coefficients and provide the probability structure for the multivariate Archimedean copulas such that the algorithm for generating random vectors with this copula can be obtained

报告题目：A PDE  Pricing Method for Double-Name Credit-Linked Notes with Counterparty Risk in Reduced-form Model with Common Shocks

报告 人：钱晓松

报告摘要：In this paper, we propose a PDE method to price a double-name credit-linked note(CLN) with counterparty risk under reduced-form framework. The default dependence among the CLN issuer and the reference entities of the double- name CLN comes from common shocks. By assuming the default intensities being directly and inversely respectively 

proportional to the interest rate which follows CIR process, we deduce explicit formulas for double-name CLNs. Additionally, we conduct some numerical experiments to examine how parameters affect the double-name CLN values. Also, credit valuation adjustment (CVA) are investigated.

报告题目：Lack of Fit Test for Infinite Variation Jumps at High Frequencies

报告 人：孔新兵

报告摘要：In this paper, we are concerned with testing for infinite variation jumps in addition to a continuous local martingale component driven by Brownian motion using high-frequency data. We developed a lack of fit type test based on the empirical distribution of the ``devolatized" increments. Under the null that the jump component is of finite variation, the empirical distribution function of the ``devolatized" increments converges to the c.d.f. of a standard normal distribution in finite dimensional distribution with a rate arbitrarily close to $/sqrt{n}$. Under the alternative hypothesis that the jumps are of infinite variation, the empirical process explodes asymptotically. Theoretical results show good performance of the size and power. Simulation studies justify the theory. A real financial data set is analyzed.

报告题目： A regime-swishing pairs trading rule

报 告 人：白洋

报告摘要：Ganapathy Vidyamurthy在《Pairs Trading: Quantitative Methods and Analysis》一书中定义配对交易为两种类型：一类是基于统计套利的配对交易，一类是基于风险套利的配对交易。基于统计套利的配对交易策略是一种市场中性策略，具体的说，是指从市场上找出历史股价走势相近的股票进行配对，当配对的股票价格差（Spreads）偏离历史均值时，则做空股价较高的股票同时买进股价较低的股票，等待他们回归到长期均衡关系，由此赚取两股票价格收敛的报酬。基于风险套利的配对交易发生在两个公司兼并时。这里我们研究的是基于统计套利的配对交易，主要的问题是配对的股票价格差长期偏离历史均值（有时在一般交易策略中被判定为失效），但是很可能股票价格差的历史均值和波动率达到一个新的水平，在新的水平下围绕均值波动。

Bock和Mestel(2008)在《A regime-switching relative value arbitrage》论文中指出，经济基本面的变化可能导致一般的配对交易信号失效。为了解决探测股票价差短期还是长期偏离长期均值，他们将Markov体制转换模型与统计套利结合来研究更适应经济环境的配对交易模型。研究方法类似于Tim Leung和Xin Li在《Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit》中描述的问题，我们需要寻找两个最优停时：开仓停时和平仓停时。优化目标是交易策略的单周期收益最大。目前的结果是得到单状态的解析解，以及两状态的数值解。一维解析解得到跟Tim Leung和Xin Li类似的结论，这也检验了我们方法的正确性，但是本文也有自己独特的解释；二维数值解可以把价值函数随A，B变化的形状表现出来，并且通过分析得到二维相比于一维优势的地方。

报告题目：Optimal reinsurance and investment problem in a defaultable market

报告 人：马建静

报告摘要：This paper investigates the optimal reinsurance and investment problem involving a default-able security. The insurer can purchase reinsurance and allocate his wealth among three _nancial securities: a money account, a stock and a defaultable corporate bond. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. Using techniques of stochastic control theory, we derive the corresponding HJB equation and decompose the original optimization problem into a pre-default case and a post-default case. Explicit expressions for optimal strategies and the corresponding value functions are derived, and then the veri_cation theorem is given. Finally, we present numerical examples to illustrate our results.

报告题目： Occupation times of general levy processes

报告 人：周江

报告摘要：For an arbitrary Le ?vy process X which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of X and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of X. It is believed that our results are important not only for the study of stochastic processes, but also for financial applications.

报告题目： Double-jump diffusion model for VIX: evidence from VVIX

报告 人：臧鑫

报告摘要：This work studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jumps in the logarithm of VIX, we derive a linear relationship between the stochastic volatility factor and the VVIX index. We detect the existence of a co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. Using the VVIX index as a proxy for stochastic volatility, we use the MCMC method to estimate the dynamics of VIX. Comparing nested models of VIX, we show that the jump in VIX and the volatility factor are statistically significant. The jump intensity is also stochastic. We analyze the impact of the jump factor on VIX dynamics.

报告题目： 含交易费用离散对冲误差研究

报 告 人：吴硕

报告摘要：在本文中，我们集中研究布朗运动下含交易费用离散对冲误差的发散速度。我们将对冲费用直接加在对冲策略本身所产生的误差上。其主要想法是将对冲误差分成两部分：纯粹由策略产生的误差和调整仓位所产生的交易费用。后者当对冲次数n趋于无穷时将会发散。我们将首先给出发散部分的一个上界，即对冲次数n的( √ n)型函数，随后证明含交易费用离散对冲误差的上下界均为 √ n阶，最后给出误差的一个逼近，定出 √ n前面的系数。证明中我们主要运用的技术是伊藤公式，洛比达法则，和[13]中的三个引理。随后给出的数值结果将支持我们理论证明中的结论。本文最后探讨了固定对冲次数n下总偏差最优化问题，给出了三种典型策略下总偏差的表达式，并指出总偏差最优化策略是一种特殊的递归定义策略。

报告题目：On a multi-dimensional risk model with regime switching

报告 人：王过京 

报告摘要：We consider an insurer with n (n ≥ 2) classes of insurance business. The surplus process for each class of insurance business is assumed to follow a compound Cox risk process. Assume that n surplus processes are correlated with thinning dependence and regime switching. By summing up the n surplus processes we obtain a correlated risk process.  The joint ruin probability for n classes of insurance business, the distribution of the number of the ruined business classes in a finite time interval and the Laplace transform of the ruin time of the correlated risk process are investigated. Some closed form results are obtained. Numerical examples are presented to explain how the collection of insurance risk increases the solvency of an insurer.