Workshop2019
Workshop on Financial Mathematics
Dinner 6:00- Seoul National University Faculty Club
http://www.snufacultyclub.com/
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Titles and abstracts
11:00-11:30 Stephan Sturm, Worcester Polytechnic Institute
Portfolio Optimization Using the Distribution Builder - Intertemporal Consumption and Incomplete Markets
Portfolio optimization subject to personal preferences of an economic agent is a mainstay in financial mathematics. The common way this problem is set up is via a utility function representing the agent's preferences. This supposes in practice that agents behave rationally as well as that there is a practical and tangible way to determine their utility function. An alternative approach, known as Distribution Builder, has been proposed by Goldstein, Sharpe and Blythe: investors should determine directly the distribution of the terminal payoff given their budget constraint. In this talk we first review the concept of the distribution builder and the mathematical model behind it, and then propose extensions to optimization of intertemporal consumption and in incomplete markets. This is based on ongoing joint work with Carole Bernard and Mauricio Elizalde Mejía.
11:30-12:00 Bong-Gyu Jang (장봉규), POSTECH
Does It Pay To Go Outside Your Comfort Zone?
Authors: Philip H. Dybvig (Washington University in St. Louis).., Bong-Gyu Jang (POSTECH) and Hyeng Keun Koo (Ajou University)
This paper proposes a utility model in which agents require effort to learn how to consume effectively. In this model, there is a comfort zone of consumption beyond which an agent suffers a utility loss. The agent can enlarge the comfort zone by paying learning costs. We provide a utility function with the comfort zone and learning costs. The preference represented by the utility function is state-dependent and exhibits time-varying risk aversion even though the underlying utility function is state-independent and has a constant absolute or relative risk aversion coe.fficient. We provide a solution to a consumption and investment problem with the utility function and discuss the optimal policies. We also study a two-agent pure exchange equilibrium and derive asset pricing implications.
12:00-12:30 Yong Hyun Shin (신용현), Sookmyung Women's University
The Effects of Maximum Leisure and Subsistence Consumption on Portfolio Selection and Voluntary Retirement
We study an optimal consumption-leisure, investment, and voluntary retirement problem under limited maximum leisure and subsistence consumption constraints. Specifically, we study a model in which an economic agent faces a limited maximum leisure and a downside constraint of consumption simultaneously. We construct closed-form solutions of optimal policies and an algebraic equation of optimal retirement wealth threshold using duality/martingale method and variational inequality methods. We perform sensitivity analyses on our model to examine the effects of maximum leisure and subsistence consumption constraints. We show that an increase in the maximum leisure and the subsistence consumption constraints reduce optimal rate of risky asset investment before retirement. Meanwhile we observe that the maximum leisure rate and the subsistence consumption constraints have a conflicting impact on optimal retirement wealth threshold. This is joint work with Kyunghyun Park (Seoul National Univ.) and Hyoseob Lee (Korea Capital Market Institute).
12:30-1:00 Kyoung-Kuk Kim (김경국), KAIST
Understanding Multi-market Microstructure using Machine Learning Approaches
In this work, we investigate market behaviors at high-frequency using neural networks trained with order book data. Experiments are done intensively with spot market data, futures data, and trading log data of a liquidity provider in South Korea. From extensive experiments, we study the lead-lag relationship between spot and futures markets and the preferences of traders with respect to P/L, inventory costs, and LP constraints. For this research, we implemented supervised learning and inverse reinforcement learning techniques. (Based on the joint works with Geonhwan Ju and Dong-Young Lim)
2:00-2:30 Kiseop Lee (이기섭), Purdue University
A financial market of a stochastic delay equation
We propose a stochastic delay financial model which describes infuences driven by historical events. The underlying is modeled by stochastic delay differential equation (SDDE), and the delay effect is modeled by a stopping time in coefficient functions. While this model makes good economical sense, it is difficult to mathematically deal with this. Therefore, we circumvent this model with similar delay effects but mathematically more tractable, which is by the backward time integration. We derive the option pricing equation and provide the option price and the perfect hedging portfolio.
2:30-3:00 Jaehyuk Choi (최재혁), Peking University HSBC business School
Finite mixture model approximation for the SABR distribution
In this paper, we represent the stochastic-alpha-beta-rho (SABR) model distribution as a parsimonious finite mixture of base models: Black-Scholes-Merton model (beta=1), Bachelier (beta=0), and constant-elasticity-of-variance (rho=0). With mixture model approach, European option prices and Greeks under the SABR model are computed as the weighted sum of those under the base model and Monte-Carlo simulations are performed easily. The mixture model parameters are obtained from the terminal volatility and integrated variance pairs evaluated with leading orders of the Karhunen-Loeve expansion of Brownian bridge and Gaussian quadrature. Numerical examples demonstrate the accuracy and efficiency of the method.
3:00-3:30 Ji-Hun Yoon (윤지훈), Pusan National University
An explicit closed-form analytic correction to an vulnerable option price using double Mellin transforms
In this paper, we derive an explicit closed-form formula of a second-order approximation for a vulnerable option price under stochastic elasticity of variance (SEV) model mentioned in (J.-H. Kim, J Lee, S.-P. Zhu, S.-H. Yu, A multiscale correction to the Black-Scholes formula, Appl. Stoch. Model. Bus. 30 (2014)). To find the explicit form correction to the vulnerable option price, we use double Mellin transform techniques. Furthermore, we analyze the behaviors of the vulnerable SEV option price in terms of the model parameters and also demonstrate that our corrected closed-form solution becomes an accurate approximation by making a comparison between our solution and the solution from the Monte Carlo simulations.
4:00-4:30 Minsuk Kwak (곽민석), Hankuk University of Foreign Studies
Financial decisions with consumption-to-income ratio constraint
We study the optimal consumption and investment decision of a wage earner with stochastic income in the presence of a constraint that imposes minimum consumption-to-income ratio. There exists a threshold of wealth to income ratio that corresponds to the consumption-to-income ratio constraint, and if the wealth-to-income ratio is below the threshold, it is optimal to keep the optimal consumption-to-income ratio as the constrained level, which can be higher than the optimal level without constraint. The optimal consumption-to-income ratio when the wealth-to-income ratio is above the threshold is lower than that without constraint. Regarding the optimal investment, we can show that, depending on the level of risk aversion and the volatility of stochastic income, tighter constraint may lead to more investment, which is consistent with Ahn, Choi, Lim (2018) that consider debt-to-income ratio constraint. We further consider the case with both consumption-to-income ratio constraint and debt-to-income ratio constraint, and investigate the interplay of two constraints.
4:30-5:00 Jin Hyuk Choi (최진혁), UNIST
Optimal termination and strategic espionage
We consider a continuous time game between a suspect and a defender. The suspect can be either an attacker or an innocent, and the defender is not informed about the suspect's type. The attacker chooses attack intensity to maximize her expected profit, and the defender chooses when to ban the suspect based on the noisy observation of suspect's action stream. In the equilibrium, the defender bans the suspect when the updated suspicion level is above a certain threshold. The model implies that the attacker does not mind revealing herself when the defender can almost perfectly observe her actions. In case the attacker is "irrational", the defender bans the suspect at the higher threshold compared to the case that the attacker is "strategic". If the defender's monitoring is costly, the defender chooses to observe the signal only if his initial suspicion level is in the middle range.
5:00-5:30 Won Se Kim (김원세), Seoul National University
Investigation of ‘Flash Crash” via Topological Data Analysis (TDA)
Although there have been various trials trying to utilize TDA in many fields such as medical research, there has been few studies that apply TDA to financial data. In recent, Interestingly, Gidea, and Katz (2018) have shown that TDA can be used in forecasting market crash utilizing daily US stock market indices data: S&P 500, DJIA, NASDAQ, and Russell 2000. However, besides the market crash of the daily horizon, since the Flash Crash on 6 May 2010, showed that the market can be substantially destabilized in as little as about 30 min, analyses of market crash of the intraday-horizon also become important parts of the study of market crash. In this talk, I investigate whether the TDA methodology based on Gidea, and Katz (2018) can be used in forecasting short term market crash such as Flash Crash.