Academic Year 20182019 Previous Semesters: AY20172018 Spring 2017
Fall 2018
Date/Time/Location: 
August 30, 2018 11:0011:50 a.m. @ ECOT 226 
Speaker: 
Nils Detering (Department of Statistics and Applied Probability, University of California at Santa Barbara) 
Title: 
Managing Default Contagion In Inhomogeneous Financial Networks 
Abstract: 
The aim of this paper is to quantify and manage systemic risk caused by default contagion in the interbank market. Our results allow us to determine the impact of local shocks to the entire system and the wider economy. As a central application, we characterize resilient and nonresilient cases. In particular, for the prominent case where the network has a degree sequence without second moment, we show that a small number of initially defaulted banks can trigger a substantial default cascade. Paralleling regulatory discussions, we determine minimal capital requirements for financial institutions sufficient to make the network resilient to small shocks. It is joint work with Thilo MeyerBrandis, Konstantinos Panagiotou and Daniel Ritter (all University of Munich)

Date/Time/Location: 
September 20, 2018 11:0011:50 a.m. @ ECOT 226 
Speaker: 
Matteo Basei (Department of Industrial Engineering and Operations Research, University of California at Berkeley) 
Title: 
Nonzerosum stochastic differential games with impulse controls 
Abstract: 
We consider a general class of nonzerosum impulsive games with N players. By means of a suitable system of quasivariational inequalities, we provide a verification theorem for the equilibrium strategies and the value functions of the game. In particular, we focus on the regularity conditions required by the theorem. We then present some practical applications. Finally, we focus on some ongoing extensions and generalizations.

Date/Time/Location: 
October 18, 2018 11:0011:50 a.m. @ ECOT 226 
Speaker: 
Ruimeng Hu (Department of Statistics, Columbia University) 
Title: 
Optimal Portfolio under Fractional Stochastic Environments 
Abstract: 
Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (nonMarkovian) fractional stochastic environment (for all Hurst index H \in (0,1)). We rigorously establish a firstorder approximation of the optimal value, where the return and volatility of the underlying asset are functions of a stationary slowly varying fractional OrnsteinUhlenbeck process. We prove that this approximation can be also generated by a fixed zeroth order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Similar results are also obtained under fast meanreverting fractional stochastic environment. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this fixed strategy in a specific family of admissible strategies.

Date/Time/Location: 
October 25, 2018 11:0011:50 a.m. @ ECOT 226 
Speaker: 
Yerkin Kitapbayev (Sloan School of Management, MIT) 
Title: 
American option pricing under stochastic volatility models via Picard iterations 
Abstract: 
This paper studies the valuation of American options for a general onefactor stochastic volatility model. Using the local timespace calculus on surfaces we derive an early exercise premium representation for the option price, parametrized by the optimal exercise surface. The exercise surface is the unique solution to an integral equation of Volterra type. The paper proposes a new numerical scheme to solve the integral equation based on the Picard iterations method. The method is flexible and can handle a wide class of nonaffine models. Performance is illustrated for the BlackScholes, Heston and 3/2 models. The approach provides fast convergence, simple implementation and good runtime/RMSE tradeoff and can be extended to other multidimensional stopping problems (joint work with J. Detemple and L. Zhang). 
Date/Time/Location: 
November 8, 2018 11:0011:50 a.m. @ ECOT 226 
Speaker: 
Joshua Aurand (Department of Applied Mathematics, University of Colorado Boulder) 
Title: 
EpsteinZin Utility Maximization over Random Horizon 
Abstract: 
This talk focuses on solving the consumptioninvestment problem for an agent with stochastic differential utility of
EpsteinZin type. In contrast to prior literature, our time horizon is
random, taken from the class of stopping times in the augmented Brownian
filtration. Parameter specification is empirically relevant, with both
relative riskaversion and the elasticity of intertemporal substitution (EIS) in
excess of one. The theory of BSDE (backward stochastic differential
equations) is used to establish existence and uniqueness of the
continuation value process, while martingale method is employed to
derive optimal strategies. Relevant examples in decision theory will be
discussed (Joint work with YuJui Huang).

Date/Time/Location: 
November 29, 2018 11:0011:50 a.m. @ ECOT 226 
Speaker: 
Saeed Khalili (Department of Mathematics, University of Colorado Boulder) 
Title: 
Optimal Consumption in the Stochastic Ramsey Problem without Boundedness Constraints 
Abstract: 
This paper investigates optimal consumption in the stochastic Ramsey problem with the CobbDouglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A nonstandard stochastic differential equation, with neither Lipschitz continuity nor linear growth, specifies the dynamics of the controlled state process. A mixture of probabilistic arguments are used to construct the state process, and establish its nonexplosiveness and strict positivity. This leads to the optimality of a feedback consumption process, defined in terms of the value function and the state process. Based on additional viscosity solutions techniques, we characterize the value function as the unique classical solution to a nonlinear elliptic equation, among an appropriate class of functions. This characterization involves a condition on the limiting behavior of the value function at the origin, which is the key to dealing with unbounded consumptions. Finally, relaxing the boundedness constraint is shown to increase, strictly, the expected utility at all wealth levels (Joint work with YuJui Huang). 
Date/Time/Location: 
December 13, 2018 11:0011:50 a.m. @ ECOT 226 
Speaker: 
Tien Khai Nguyen (Department of Mathematics, North Carolina State University) 
Title: 
A Stochastic Model of Optimal Debt Management and Bankruptcy 
Abstract: 
Consider a problem of optimal debt management which is modeled as a noncooperative game between a borrower and a pool of riskneutral lenders. Since the debtor may go bankrupt, lenders charge a higher interest rate to offset the possible loss of part of their investment. In this talk, I will present results on existence and properties of optimal strategies, both in a deterministic and in a stochastic framework. 

