Title and Abstract
Hyeng Keun Koo (Ajou University)
Hyeng Keun Koo (Ajou University)
Title : Lifetime Portfolio Choice with Costly Adjustment for Living Standards
Title : Lifetime Portfolio Choice with Costly Adjustment for Living Standards
Abstract: In this paper we examine a model of lifetime portfolio choice over a finite horizon that incorporates adjustment costs for living standards. The model proposes a smooth and consistent payout policy and provides an easily calculable analytic solution, which enhances its potential for practical asset management applications. Additionally, it produces two testable implications: (i) a pattern of declining consumption and (ii) increasing risk aversion in the later stages of individual investors' lives. We approach the optimization problem by combining four key methodologies: (i) the dual martingale approach, (ii) transformation to optimal switching problems, (iii) the partial differential equation techniques (in particular, the theory of obstacle problems), and (iv) the Skorokhod lemma. This talk is based on joint work with Junkee Jeon and Jehan Oh.
Abstract: In this paper we examine a model of lifetime portfolio choice over a finite horizon that incorporates adjustment costs for living standards. The model proposes a smooth and consistent payout policy and provides an easily calculable analytic solution, which enhances its potential for practical asset management applications. Additionally, it produces two testable implications: (i) a pattern of declining consumption and (ii) increasing risk aversion in the later stages of individual investors' lives. We approach the optimization problem by combining four key methodologies: (i) the dual martingale approach, (ii) transformation to optimal switching problems, (iii) the partial differential equation techniques (in particular, the theory of obstacle problems), and (iv) the Skorokhod lemma. This talk is based on joint work with Junkee Jeon and Jehan Oh.
Johannes Langner (Leibniz Universität Hannover)
Johannes Langner (Leibniz Universität Hannover)
Title : Markov-Nash Equilibria in Mean-Field Games under Model Uncertainty
Title : Markov-Nash Equilibria in Mean-Field Games under Model Uncertainty
Abstract: In this talk we present a new approach for a mean-field equilibrium under model uncertainty. Our results are inspired by and can be seen as the distributionally robust analog of – the work of Saldi et al. (SIAM J. Control Optim. 56:6, 4256-4287, 2018). In a discrete time dynamic mean-field game with N agents, the empirical state-distribution of those agents affects their individual rewards and state transition probabilities, which we assume to be uncertain. It is the objective of each agent to choose the optimal Markov policy to maximize their worst-case expected rewards under consideration of the empirical distribution. We show the existence of the mean-field equilibrium in the infinite population limit $N →\infty$ . In analogy to Saldi et al., we demonstrate that an approximate of a Markov-Nash equilibrium can be obtained by using the mean-field equilibrium in the infinite population. This talk is based on joint work with Ariel Neufeld and Kyunghyun Park.
Abstract: In this talk we present a new approach for a mean-field equilibrium under model uncertainty. Our results are inspired by and can be seen as the distributionally robust analog of – the work of Saldi et al. (SIAM J. Control Optim. 56:6, 4256-4287, 2018). In a discrete time dynamic mean-field game with N agents, the empirical state-distribution of those agents affects their individual rewards and state transition probabilities, which we assume to be uncertain. It is the objective of each agent to choose the optimal Markov policy to maximize their worst-case expected rewards under consideration of the empirical distribution. We show the existence of the mean-field equilibrium in the infinite population limit $N →\infty$ . In analogy to Saldi et al., we demonstrate that an approximate of a Markov-Nash equilibrium can be obtained by using the mean-field equilibrium in the infinite population. This talk is based on joint work with Ariel Neufeld and Kyunghyun Park.
Ariel Neufeld (Nanyang Technological University)
Ariel Neufeld (Nanyang Technological University)
Title : Markov Decision Processes under Model Uncertainty
Title : Markov Decision Processes under Model Uncertainty
Abstract: In this talk we introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account. This talk is based on joint work with Julian Sester and Mario Šikić
Abstract: In this talk we introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account. This talk is based on joint work with Julian Sester and Mario Šikić
A. Max Reppen (Boston University)
A. Max Reppen (Boston University)
Title : Segmented Trading Markets
Title : Segmented Trading Markets
Abstract: We study competition and endogenous fragmentation among heterogenous trading venues that differ in technology (fast vs. slow), where traders can dynamically choose which venue to trade in. We show that technological improvements increase trading speed, but may also heighten differentiation, which reduces competition, leads to higher trading fees, and potentially reduces trading volume and welfare. Improvements in the slower venue lead to increased trading speed, decreased differentiation, and thus increased trading volume and welfare. Conversely, the effect of improvements in the faster venue is generally ambiguous and depends on the extent of traders’ patience, the frequency of their preference shocks, and the competition between venue owners. We further study the effect of technological improvement in one of the venues when both initially have the same trading speed. We find that if the trading speeds are initially slow enough, the technological improvement will increase trading volume and trader welfare. Conversely, if the trading speeds are initially fast, the increase in trading fees outweighs the speed advantage that comes with technological improvement, leading to decreased trading volume and trader welfare.
Abstract: We study competition and endogenous fragmentation among heterogenous trading venues that differ in technology (fast vs. slow), where traders can dynamically choose which venue to trade in. We show that technological improvements increase trading speed, but may also heighten differentiation, which reduces competition, leads to higher trading fees, and potentially reduces trading volume and welfare. Improvements in the slower venue lead to increased trading speed, decreased differentiation, and thus increased trading volume and welfare. Conversely, the effect of improvements in the faster venue is generally ambiguous and depends on the extent of traders’ patience, the frequency of their preference shocks, and the competition between venue owners. We further study the effect of technological improvement in one of the venues when both initially have the same trading speed. We find that if the trading speeds are initially slow enough, the technological improvement will increase trading volume and trader welfare. Conversely, if the trading speeds are initially fast, the increase in trading fees outweighs the speed advantage that comes with technological improvement, leading to decreased trading volume and trader welfare.
Alessandro Sgarabottolo (Universität Bielefeld)
Alessandro Sgarabottolo (Universität Bielefeld)
Title : Discrete Approximation of Risk-Based Pricing under Uncertainty
Title : Discrete Approximation of Risk-Based Pricing under Uncertainty
Abstract: We discuss the limit of risk-based prices of European contingent claims in discrete-time financial markets under volatility uncertainty when the number of intermediate trading periods goes to infinity. The limiting dynamics are obtained using recently developed results for the construction of strongly continuous convex monotone semigroups. We connect the resulting dynamics to the semigroups associated to G-Brownian motion, showing in particular that the worst-case bounds always give rise to a larger bid-ask spread than the risk-based bounds. Moreover, the worst-case bounds are achieved as limit of the risk-based bounds as the agent’s risk aversion tends to infinity. The talk is based on joint work with Jonas Blessing and Michael Kupper.
Abstract: We discuss the limit of risk-based prices of European contingent claims in discrete-time financial markets under volatility uncertainty when the number of intermediate trading periods goes to infinity. The limiting dynamics are obtained using recently developed results for the construction of strongly continuous convex monotone semigroups. We connect the resulting dynamics to the semigroups associated to G-Brownian motion, showing in particular that the worst-case bounds always give rise to a larger bid-ask spread than the risk-based bounds. Moreover, the worst-case bounds are achieved as limit of the risk-based bounds as the agent’s risk aversion tends to infinity. The talk is based on joint work with Jonas Blessing and Michael Kupper.