[01065] Mathematics and its Applications of Risk and Decision
Session Time & Room : 4E (Aug.24, 17:40-19:20) @D501
Type : Proposal of Minisymposium
Abstract : In the age of uncertainty highlighted by events such as the financial crisis and the outbreak of COVID-19, policy makers need to acquire a holistic yet rigorous understanding of decision making under risk. This symposium aims to bring together academic researchers of diverse background to showcase the latest development of the mathematical theories and applications for risk and decision. The covered topics include stochastic control, optimal decision-making, model uncertainty and their applications in fields like economics and insurance. The collective effort of the expert speakers from this symposium will constitute impactful decision protocols and policy implications.
[04299] Optimal reinsurance with multivariate risks and dependence uncertainty
Format : Talk at Waseda University
Author(s) :
Tolulope Rhoda Fadina (University of Essex)
Tolulope Fadina (University of Essex)
Abstract : We study the optimal reinsurance design from the perspective of an insurer with multiple lines of business, where the
reinsurance is purchased by the insurer for each line of business respectively. For the risk vector generated by the
multiple lines of business, we suppose that the marginal distributions are fixed, but the dependence structure between
these risks is unknown. Due to the unknown dependence structure, the optimal strategy is investigated for the
worst-case scenario. We consider two types of risk measures: Value-at-Risk (VaR) and Range-Value-at-Risk including Expected Shortfall as a special case, and general premium principles satisfying certain conditions. To be more
practical, the minimization of the total risk is conducted with both budget constraints and expected profit constraints.
For the VaR-based model with only two risks, it turns out that the limited stop-loss reinsurance treaty is optimal for
each line of business. For the model with more than two risks, we obtain two types of optimal reinsurance strategies if the marginals have convex or concave distributions on their tail parts by constraining the ceded loss functions to be
convex or concave.
[04329] Irreversible consumption habit under ambiguity: Singular control and optimal G-stopping time
Format : Talk at Waseda University
Author(s) :
HOI YING WONG (The Chinese University of Hong Kong)
Kyunghyun Park (Nanyang Technological University)
Kexin Chen (The Hong Kong Polytechnic University)
Abstract : Consider robust utility maximization with an irreversible consumption habit, where an agent concerned about model ambiguity is unwilling to decrease consumption and must simultaneously contend with a disutility (i.e., an adjustment cost) due to a consumption increase. While the optimization is a robust analog of singular control problems over a class of consumption-investment strategies and a set of probability measures, it is a new formulation that involves non-dominated probability measures of the diffusion process for the underlying assets in addition to singular controls with an adjustment cost. This paper provides a novel connection between the singular controls in the optimization and the optimal G-stopping times in a G-expectation space, using a duality theory. This connection enables to derive the robust consumption strategy as a running maximum of the stochastic boundary, which is characterized by a free boundary arising from the optimal G-stopping times. The duality, which relies on arguments based on reflected G-BSDEs, is achieved by verifying the first-order optimality conditions for the singular control, the budget constraint equation for the robust strategies, and the worst-case realization under the non-dominated measures.
[05330] On/Off Shore Currency Rate Discrepancy
Format : Talk at Waseda University
Author(s) :
Samuel Drapeau (Shanghai jiao Tong university )
Xuan Tao (Shanghai Jiao Tong University)
Abstract : Most developing countries (especially in Asia) adopted a tight control of foreign capital in order to protect their economy from abrupt capital outflows in period of crisis.
As those economies developed and opened up to foreign financial investment, they often set up off shore currency exchange markets to facilitate the transfer of capital.
This is for instance the case of China where the on shore rmb (CNY) was complemented with an off shore market for trading this currency (CNH).
Theoretically, the face value from a domestic viewpoint of the currency is the same regardless of on/off shore origin.
And indeed, when observing the spot rate, the CNY and the CNH rate only differ marginally.
However, when looking at the price of futures for longer maturity, there is a significant discrepancy (in the CNY/CNY case, up to 4% when corrected for maturity).
This is puzzling as the future face value follows the same principle as the present one.
In the present work we propose a continuous time equilibrium in two similar market which are scholastically coupled.
This solution of which is given by a coupled quadratic jump diffusion FBDE that provide an equilibrium price on both markets.
We then use a second equilibrium to price futures and therefore provide some interpretations as for the price discrepancy observed on the market.
This is a joint work with Xuan Tao, Peng Luo, Wang Tan and Wang Tao
[04244] Portfolio Selection, Periodic Evaluations and Risk Taking
Format : Talk at Waseda University
Author(s) :
Alex Sing-lam Tse (University College London)
Harry Zheng (Imperial College London)
Abstract : We present a continuous-time portfolio selection problem faced by an agent with S-shaped preference who maximizes the utilities derived from the portfolio's periodic performance over an infinite horizon. The periodic reward structure creates subtle incentive distortion. In some cases, local risk aversion is induced which discourages the agent from risk taking in the extreme bad states of the world. In some other cases, eventual ruin of the portfolio is inevitable and the agent underinvests in the good states of the world to manipulate the basis of subsequent performance evaluations. We outline several important elements of incentive design to contain the long-term portfolio risk.
