为了加强随机分析、金融数学与保险精算领域研究生间学术交流，由苏州大学联合上海交通大学举办的《随机分析、金融数学与保险精算研究生论坛》，将于2019年5月17日-18日在苏州举行。本次研讨会将讨论随机分析与概率论，金融数学与金融工程，金融风险管理，保险精算等领域的前沿问题与最新研究进展。

**主****办单位**

苏州大学金融工程研究中心

**协办单位**

上海交通大学数学科学学院

**地点**

苏州市姑苏区十梓街1号苏州大学览秀楼105报告厅

**会议联系人 **

苏州大学 穆蕊（18136064623）rmu@suda.edu.cn

上海交通大学 林一青 yiqing.lin@sjtu.edu.cn

**参会人员列表（按姓氏拼音排序）**

姓名 | 单位 |

陈昕 | 上海交通大学 |

Samuel Drapeau | 上海交通大学 |

林一青 | 上海交通大学 |

穆 蕊 | 苏州大学 |

裴梓婷 | 苏州大学 |

钱晓松 | 苏州大学 |

秦聪 | 苏州大学 |

Mekonnen Tadese | 上海交通大学 |

陶璇 | 上海交通大学 |

王过京 | 苏州大学 |

王希舜 | 苏州大学 |

徐玉红 | 苏州大学 |

叶文杰 | 上海交通大学 |

岳兴业 | 苏州大学 |

赵卉 | 上海交通大学 |

支康权 | 苏州大学 |

周从金 | 苏州大学 |

张静 | 复旦大学 |

张云博 | 上海交通大学 |

**程序**

5月 17日 | 时间 | 主持人 | 报告人 | 报告题目 |

10：00-10：25 | 签到、领取会议材料 | |||

10：25-10：30 |
| 王过京 | 致开幕词 | |

10：30-10：55 | 穆蕊 | 叶文杰 | Exact Controllability of Linear Mean-Field Stochastic Systems and Observability Inequality for Mean-Field BSDEs | |

11：00-11：25 | 周从金 | The Valuation of Mortgage Pass-Through Securities with Partial Prepayment Risk | ||

11：30-12：00 |
张云博 | Pricing and Hedging Performance of Pegged FX Markets Based on Regime Switching Model. | ||

12：00-13：45 | 午餐 | |||

13：45-14：10 | 林一青 | Mekonnen Tadese | Relative Bound and Asymptotic Comparison of Expectile with Respect to Expected Shortfall | |

14:15-14:40 | 裴梓婷 | Risk Management by GVaR | ||

14:45-15:10 | 支康权 | Basket Credit Derivatives Pricing in a Markov Chain Model with Interacting Intensities and Contagion Risk | ||

15:15-15:35 | 茶歇 | |||

15:35-16:00 | 徐玉红 | 王希舜 | Dynmaic Mean-Variance Asset Allocation in Ambiguous Market–Illustated by the Case of CEV Model | |

16:05-16:30 | 赵卉 | A Study on Parameter Estimation with Mean Uncertainty under $G$-Framework | ||

16:35-17:00 | 陶璇 | On Detecting Spoofing Strategies in High Frequency Trading | ||

18：00 | 晚宴 | |||

5月 18日 | 9：00-11：00 | 苏州大学上海交通大学博士生 金融数学与保险精算主题圆桌论坛 |

**报告题目与摘要**

**Exact Controllability of Linear Mean-Field Stochastic Systems and Observability Inequality for Mean-Field BSDEs**

**Wendie Ye ****（叶文杰）**

In this paper we study the controllability of the linear mean-field stochastic system with time-varying random coefficients. We use the observability inequality as an important tool to deal with the exact controllability problem. Finally, we obtain the equivalence relation between $L^2$-exact controllability and $L^2$-observability inequality. As an application, we use the previous results to give the optimal control of the norm optimal control problem.

**The Valuation of Mortgage Pass-Through Securities with Partial Prepayment Risk**

**Congjun Zhou****（周从金）**

We develop valuation models for both a mortgage contract and mortgage pass-through securities with partial prepayment risk using an intensity-based approach. The occurrence time of the prepayments is modeled as a Poisson process. We assume that the ratio of the prepayment balance to the resulting outstanding balance at the partial prepayment time is a continuous function. Under these conditions, we calculate the payment rate and prepayment balance of the mortgagor at the prepayment time. Similarly, we get the cash flow that investors received from the underlying mortgage pool. Valuation formulas for mortgage contracts and mortgage pass-through securities are derived when we allow the interest rate to switch in different regimes. Finally, we give some numerical examples.

**Pricing and Hedging Performance of Pegged FX Markets Based on Regime Switching Model.**

**Yunbo Zhang (****张云博）**

Foreign exchange markets are the largest and most liquids in the world. Any classical model for pricing and hedging of derivatives assumes a free floating exchange rate. However, a consequent number of foreign exchanges are eventually pegged bringing some puzzling facts in terms of prices. Drapeau, Wang and Wang (2019) proposed an economically motivated particular regime-switching model to explain this puzzle and provide pricing and calibration of parameters to data. Following this work, we deepen the quantitative analysis by providing pricing and hedging formulas for this regime switching model using classical and Fourier techniques. We then derive and compare numerically the performance of different hedging strategies: Black and Scholes delta hedging, regime switching delta hedging, as well as mean variance hedging. The comparison is first performed and discussed on simulated data and then applied to the HKD-USD pegged market (daily 2014-2019). We design a recalibration procedure to fit the volatility surface, study the term structure of the parameters, and compare the different hedging strategies. The classical SABR model is used as a benchmark showing that the regime switching calibration performs better in this situation. It turns out that in terms of accuracy and computational costs the regime switching together with a Fourier method is the better approach in terms of pricing and hedging.

Joint work with Samuel Drapeau

**Relative Bound and Asymptotic Comparison of Expectile with Respect to Expected Shortfall**

**Mekonnen Tadese**

Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty equivalent. Lower and upper bounds of expectile are derived in terms of expected shortfall as well as a characterization of expectile in terms of expected shortfall. Further, we study the asymptotic behavior of expectile with respect to expected shortfall as the risk level goes to $0$ in terms of extreme value distributions. Illustrating the formulation of expectile in terms of expected shortfall, we also provide explicit or semi-explicit expressions of expectile for some classical distributions.

**Risk Management by GVaR**

**Ziting Pei****（裴梓婷）**

A kind of worst-case value-at-risk, GVaR, is defined to measure risk incorporating first- and second-order moments uncertainty. Compared with most extant notions of worst-case VaR, GVaR can be computed by an explicit formula, and can be applied to large portfolios of several hundreds dimensions. It is robust for, but not limited to a set of VaRs based on normal distributions. We also reveal connections to robust portfolio optimization, which provides a tractable way to give optimal allocations under model uncertainty. Empirical analysis demonstrates that GVaR is a robust risk measure.

**Basket Credit Derivatives Pricing in a Markov Chain Model with Interacting Intensities and Contagion Risk**

**Kangquan Zhi****（支康权）**

We analyze basket credit derivative contracts (BCDS and BCLN) with counterparty risk using a markov chain interacting intensities with contagion model. We assume the default intensities of the protection seller and the references are affected by an external shock event and contagion risk. The arrival of the shock event is a Cox process whose stochastic intensity is an affine diffusion process with jumps. We derive a recursive formula for the joint default probability of reference assets. The pricing formulas of BCDS and BCLN are presented. We also examine how the correlated default risks between the protection seller and the underlying entity may affect the premium rates.

**Dynmaic Mean-Variance Asset Allocation in Ambiguous Market–Illustated by the Case of CEV Model**

**Xishun Wang****（王希舜）**

There are two different manifestations of the uncertainty of the event. One isabout the uncertainty of the event with a probability, that is, randomness ; the other is about the uncertainty of the event probability, that is, ambiguity. In the study of risk management, the uncertainty about financial market is mainly focused on randomness. So far, most of asset allocation models take randomness as the uncertainty. We consider that dynamic mean-variance asset allocation in ambiguous markets. Trading may take place continuously in two securities: a riskless bond and a risky stock. Assuming that the stock market is an ambiguous market, but it has two basic states: bull market and bear market . Investor has a subjective probability to predict which basic market would occur, and aims to maximize the expected benefit and minimize the variance in every basic market. So how should the investor allocate asset now? We take the weighted mean-variance of basic market as the utility function of ambiguous market, deriving the time-consistent optimal portfolio strategy and coupled PDEs of the expected return in ambiguous markets, and simulating the result by explicit difference method with CEV model as an example. The numerical results show that our model is meaningful , and the optimal strategy is not a simple weighted value of each optimal strategy in two unambiguous markets.

**A Study on Parameter Estimation with Mean Uncertainty under $G$-Framework**

**Hui Zhao ****（赵卉）**

This talk studies the implementations of two approaches to parameter estimation with mean uncertainty in a nonlinear expectation framework. First, we apply the min-mean/max-mean method to estimate the optimal unbiased estimators for maximal distribution in an asymptotic sense. Secondly, consider the mean uncertainty of residual errors, the classical linear regression model can be modified as an upper expectation regression model with the aid of machine learning algorithms, which can be effective for robust estimations. By means of simulation and real data analysis, the talk presents the applications of the two approaches from nonlinear expectation Statistics compared with those of classical counterparts.

**On Detecting Spoofing Strategies in High Frequency Trading**

**Xuan Tao (****陶璇）**

The development of high frequency and algorithmic trading allowed to reduce considerably the bid ask spread by increasing liquidity in limit order books. Beyond the problem of optimal placement of market and limit orders, the possibility to cancel orders for free leaves room for price manipulation, in particular for spoofing strategies. It is an empirical evidence that volume imbalance on both side of the limit order book reflecting offer and demand has an impact on subsequent price movements. Spoofers use this effect to artificially modify the imbalance by posting limit orders and then execute market orders at subsequent better prices while canceling at a high speed their previous limit orders. In this work we set up a model to determine where a spoofer would place its limit orders to maximize its gains as a function of the imbalance impact on the price movement. We study the solution of this non local optimization problem as a function of the imbalance. With this at hand, we calibrate on real data from TMX the imbalance as a function of its depth and and recent history to a mixture binomial distribution of the resulting price movement. Based on this calibration and results, we then provide some methods as how to detect within the limit order book eventual spoofing behavior while the real trader ID is (partially) unknown.

Joint work with Samuel Drapeau (SJTU), Lan Ling (SJTU) and Andrew Day (Western University)