由18新利体育 金融工程研究中心举办的“2019年金融数学与金融工程青年学者研讨会”将于2019年9月25日-27日在18新利体育 （苏州）举行。本次研讨会旨在邀请国内外同行青年学者报告交流金融数学与金融工程领域的最新科研进展，以了解学术动态，促进学术交流和相关学科发展。

主办单位

苏州大学金融工程研究中心

学术和组织委员会

王过京、岳兴业、钱晓松、徐玉红、穆蕊

会议地点

苏州市姑苏区十梓街1号18新利体育 览秀楼105报告厅，校北门向南直行至钟楼西侧精蕴楼北侧，步行约15分钟。

住宿地点

苏州市姑苏区十全街滚绣坊20号南林饭店山水楼大厅。

电话：0512-68017888

会议联系人

穆蕊（18136064623）rmu@suda.edu.cn

支康权（15152091178） zhikangquan96@163.com

会议费用

1.参会代表免交注册费、提供午餐和晚餐，承担参会代表的住宿费。

2.如需要，会议支付参会代表的往返差旅费

参会人员列表（按姓氏拼音排序）

程序

报告题目与摘要

不完备市场下的福利经济学定理及汇总问题

马成虎（复旦大学管理学院财务金融系）

本文证明了不完备市场环境下完全竞争市场所支持的均衡资源分配必满足股权分置意义下的“受限”Pareto 最优的性质，从而完善了不完备市场环境下的福利经济学理论。文中构建的决定均衡资产定价率的“代表性股民效用函数”，综合了所有个体交易者效用函数，并刻画了由于市场非完备性给诸个体投资者带来的福利损耗。该效用函数的构建标志着自上世纪60年代以来困扰经济学界近半个世纪的不完备市场环境下的“汇总问题”得以解决，为基于代表性投资者偏好的一般均衡资产定价理论奠定了基础

Valuation of Risk-Based Premium of DB Pension Plan with Terminations

钱林义（华东师范大学经济与管理学部统计学院）

This paper concentrates on the premium valuation of pension insurance provided by the Pension Benefit Guaranty Corporation (PBGC). Such an insurance instrument allows a defined benefit pension sponsor to receive protection from the PBGC in case that the pension fund fails to make pension payments as promised or that the plan sponsor does not stay in business any more. In practice, both pension fund and sponsor assets play critical role in terms of pension payment, and it is not reasonable to isolate the risk of distress termination of sponsor assets from that of premature termination of pension fund. Different from previous works in which premature termination of pension fund and distress termination of sponsor assets are analyzed separately, our model examines the situation in which retirees suffer the two risks of termination at the same time. We evaluate the risk-based fair premium under the framework that pension fund and sponsor assets are correlated and subject to the risk of involuntary termination and distress termination, respectively, and we manage to obtain closed-form pricing formulas. Our model is more practical because of realistic design of termination schemes.Numerical simulations are also carried out to demonstrate our findings. Our numerical experiments validate that variable rate premium is a more appropriate channel for the PBGC to implement.

Optimal dividend strategy with endogenous bankruptcy boundary under Chapter 11 of the US bankruptcy code

林建伟（莆田学院数学与金融学院）

This paper concerns the optimal dividend strategy problem with endogenous bankruptcy boundary under the presence of Chapter 11 of the US bankruptcy code. For any given declaring bankruptcy boundary under Chapter 11, we model the value function as the solution to a singular stochastic control problem and its corresponding closed-form solution is obtained by partial differential equation. Meanwhile, we prove that the optimal dividend strategy for any given bankruptcy boundary is a barrier strategy constructed by a unique reflecting barrier. The optimal bankruptcy boundary is numerically determined by maximizing the value function. Numerical results show that Chapter 11 has a role impact on the optimal dividend strategy problem. The company can get the bigger total value by filing for Chapter 11; The company pays dividends to shareholders earlier to maximize the total value of the company, but the expected liquidation time is shorter.

Optimal Switching under a Hybrid Diffusion Model and Applications to Stock Trading

吕思宇（东南大学数学学院）

This talk is concerned with the optimal switching problem under a hybrid diffusion (or, regime switching) model in an infinite horizon. The state of the system consists of a number of diffusions coupled by a finite-state continuous-time Markov chain. Based on the dynamic programming principle, the value function of our optimal switching problem is proved to be the unique viscosity solution to the associated system of variational inequalities. The optimal switching strategy, indicating when and where it is optimal to switch, is given in terms of the switching and continuation regions. In many applications, the underlying Markov chain has a large state space and exhibits two-time-scale structure. In this case, a singular perturbation approach is employed to reduce the computational complexity involved. It is shown that as the time-scale parameter $\varepsilon$ goes to zero, the value function of the original problem converges to that of a limit problem. The limit problem is much easier to solve, and its optimal switching solution leads to an approximate solution to the original problem. Finally, as an application of our theoretical results, an example concerning the stock trading problem in a regime switching market is provided. It is emphasized that, this paper is the first time to introduce the optimal switching as a general framework to study the stock trading problem, in view of their inherent connection. Both optimal trading rule and convergence result are numerically demonstrated in this example. This is a joint work with Profs Zhen Wu and Qing Zhang.

When is Systematic Risk Priced? A New Perspective from Probability Weighting

石芸（华东师范大学，经管学部，统计交叉18新利备用网站 院）

The central task of asset pricing is to examine how expected returns are related to risk. Probability weighting affects investor's perception of risk, especially the tail risk. This paper wants to examine the role of probability weighting behind asset pricing, both theoretically and empirically.On the theoretical front, we consider a one-period-two-date economy with rank-dependent utility agents. After deriving the equilibrium asset pricing formula under probability weighting, we show that in the derived three-moment-CAPM model, the existence of probability weighting is helpful in understanding both beta anomaly and coskewness pricing. On the empirical front, we first develop several indices to identify the probability weighting levels and further separate the market into two regimes: overweighting periods and underweighting periods. We find that stock's expected return is positively related to its beta risk during overweighting periods, but negatively related to its beta risk during underweighting periods. Unconditional on probability weighting, these two effects offset each other, resulting in a flat relationship between beta and return. We also find that the stock's expected return is negatively related to its co-skewness during overweighting periods but unrelated to its co-skewness during underweighting periods.

Lévy 模型下金融衍生品定价的重要抽样技术研究

马俊美（上海财经大学数学学院）

本文发展了一类有效的指数扭转重要抽样技术来减小金融产品定价的模拟误差，在一个更一般的指数测度变换框架下，基于Cauchy-Schwartz不等式和最小二乘法，提出了一个新的选取最优重要抽样密度函数的方法。并通过引入舍选抽样技术和标准化的重要抽样法分别解决了Lévy 模型下扭转测度随机数不易抽取和期望估计中归一化常数难于处理的问题。并以四类金融衍生品：欧式期权，亚式期权，波动率互换和方差期权的定价问题为例进行了数值模拟验证，结果表明算法具有高效的方差缩减效果。本文的研究结果可以进一步应用于其它非正态总体的市场模型以及其它金融衍生产品的定价问题等。

Absence of dominating probability for weakly compact probability variety

郑国强（东南大学数学学院）

Based on the Halmos-Savage theorem, a new tractable criterion isconfirmed on recognizing whether a family of probabilities can be dominated by a single probability or not, the implementation of which to the probability variety involved in $G$-expectation evinces the absence of a dominating probability. Therefore even though the static model of $G$-expectation can be constructed with the help of countably infinitely many probabilities those can be dominated simultaneously, when it comes to dynamic situation, such dominating probability measure does not exist. The key ingredient of our proof relies on the normability of Wasserstein metric of order one inprobability space.

Pricing default risk in mortgage-backed securities under a regime-switching reduced-form model

郭洁（苏州科技大学）

In this paper, we propose a reduced-form model to price default risk in mortgages and fixed-rate pass-through mortgage-backed securities. Since the default of borrowers is often affected by macroeconomic conditions, we take into account the changes of market regimes. We introduce a default factor process to model the default risk of borrowers and define its exponential decreasing rate as default rate, which follows a shot-noise process. The model assumes that the interest rate and the default rate are all influenced by macroeconomic conditions described by a homogeneous Markov chain. Explicit pricing formulas for mortgage-backed securities with defaultable underlying mortgages are obtained through the conditional Laplace transform of the regime-switching shot-noise process. Numerical illustration is also presented to show the impact of model parameters on the price.

Hermite Expansion for Transition Densities of Irreducible Diffusions with An Application to Option Pricing

万相伟（上海交通大学安泰经济与管理学院金融系）

A diffusion is said to be reducible if there exists a one-to-one transformation of the diffusion into a new one whose diffusion matrix is the identity matrix, otherwise it is irreducible. Most multivariate diffusions such as the stochastic volatility models are irreducible. As pointed out by Ait-Sahalia (2008), the straight Hermite expansion of Ait-Sahalia (2002) will not in general converge for irreducible diffusions.

In this paper we manage to develop the Hermite expansion for transition densities of irreducible diffusions, which converges as the time interval shrinks to zero. By introducing a quasi-Lamperti transform unitizing the process' diffusion matrix at the initial time, we can expand the transition density of the transformed process using Hermite polynomials as the orthogonal basis. Then we derive explicit recursive formulas for the expansion coefficients using the It\^{o}-Taylor expansion method, and prove the small-time convergence of the expansion. Moreover, we show that the derived Hermite expansion unifies some existing methods including the expansions of Li (2013) and Yang, Chen and Wan (2019). In addition, we demonstrate the advantage of Hermite expansion by deriving explicit recursive expansion formulas for European option prices under irreducible diffusions. Numerical experiments illustrate the accuracy and effectiveness of our approach.

Optimal Stopping with Random Lag

宋颖达（上海交通大学安泰经济与管理学院）

This paper is concerned with the optimal stopping problem with random time lag under general Markov processes. We solve the problem by constructing a continues-time Markov chain (CTMC) to approximate the general Markov process model and compute the solution under the CTMC. We prove the convergence our method. Based on our method, we analyze the impact of time lag with various distributions on the optimal stopping problem.

Stochastic optimal control problem with varying terminal time and related application

杨淑振（山东大学）

To establish the stochastic maximum principle for the optimal control problem under state constraints without using Ekland's variational principle, we propose a new optimal control problem, in which the terminal time follows the varying of the control via the constrained condition. Focusing on this new optimal control problem, we investigate a novel stochastic maximum principle, which differ from the traditional optimal control problem under state constraints.The optimal pair of the optimal control model can be verified via this new stochastic maximum principle. In addition, this new optimal control model can not only minimize the cost functional but also decreases the holding time.

The R Measures: A Theory of Expected Returns of Contingent Claims

卓小杨（清华大学五道口金融学院）

This paper introduces a new probability measure R for deriving the analytical solution of a contingent claim's expected price at a given finite horizon H, less than or equal to the terminal date T, on which the claim pays out a single risky cash flow. Using the R measure, we show that any model that admits an analytical solution to a contingent claim's current price will generally provide an analytical solution to the claim's expected price at the horizon H. The R measure is a hybrid measure that nests both the physical probability measure P and the risk-neutral measure Q. We also extend the R measure to RT forward measure for deriving analytical solutions of a contingent claim's expected price at a given finite horizon, when the short rate is stochastic. We present some stylized facts about the term structure of expected returns and the horizon structure of expected returns of contingent claims such as equity options, Treasuary bonds, bond options, and corporate bonds. This is a joint work with Sanjay K. Nawalkha (University of Massachusetts).

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