# 2016-Graduate Students in Actuarial Science

Organizer and Chair: Andrei Badescu (University of Toronto)
[PDF]

DONGCHEN LI, University of Waterloo
On Minimizing Drawdown Risks of Lifetime Investments  [PDF]

Drawdown measures the decline of portfolio value from its historic high-water mark. We study lifetime investment problems aiming at minimizing drawdown-related risk measures. Under the Black-Scholes framework, we examine two financial market models: a market with two risky assets, and a market with a risk-free asset and a risky asset. Closed-form optimal trading strategies are derived by solving the associated Hamilton-Jacobi-Bellman (HJB) equations. We show that it is optimal to minimize the portfolio variance when the fund value is at its historic high-water mark. Moreover, when the fund value drops, the proportion of wealth invested in the asset with a higher instantaneous rate of return should be increased.

HAIYAN LIU, University of Waterloo
Asymptotic Equivalence of Risk Measures under Dependence Uncertainty  [PDF]

We study the aggregate risk of a large inhomogeneous portfolio with dependence uncertainty, evaluated by a generic risk measure. We establish general asymptotic equivalence results for the classes of distortion risk measures and convex risk measures under different mild conditions. The results implicitly suggest that it is only reasonable to implement a coherent risk measure for an aggregate risk of a large portfolio with uncertainty in the dependence structure, a relevant situation for risk management practice.

JINGONG ZHANG, University of Waterloo
Optimal Hedging with Basis Risk under Mean-Variance Criteria  [PDF]

Optimal hedging for European options is studied under a mean-variance framework in the presence of basis risk, where the underlying asset is non-tradable and replaced by another closely related and tradable asset. The problem is formulated to determine the subgame Nash equilibrium hedging strategy. This problem differs from classic dynamic programming problems in that its objective function is not separable and therefore, the Bellman optimality principle does not apply. Optimal control process is derived by resorting to dynamic programming technique and an extended HJB equation. A closed-form optimal control process is obtained with the aid of a change-of-measure technique.

RUIXI ZHANG, Western University
On a Renewal Risk Process under a Dividend Barrier Strategy  [PDF]

We consider a renewal risk process in the presence of a constant dividend barrier. Using probabilistic arguments, the probability of ruin is shown to be~1, if either the claim sizes exceed the barrier with positive probability or 0 is a point of increase of the inter-claim time. For Kn-distributed inter-claim times, we offer a revised proof regarding the number of roots to the generalized Lundberg's equation. The density and moments of the time to ruin are approximated numerically for generalized Erlang(n) inter-claim times and rational-distributed claim sizes. However, if neither condition is satisfied, the probability of ruin may be reduced to~0. A dividend-reinsurance strategy inspired by the last observation is discussed. Finally, generalizations to certain dependent risk processes are included.

MOHAMED AMINE LKABOUS, Université du Québec à Montréal
Parisian ruin for a refracted Lévy process  [PDF]

Parisian ruin occurs if the time spent below zero by the risk process is longer than a fixed delay. In this talk, we investigate Parisian ruin for a refracted Lévy process. We generalize the result of Loeffen, Czarna and Palmowski (2013) for the probability of Parisian ruin of a standard Lévy insurance risk process. Other fluctuation identities with Parisian delay will be presented. Finally, we will give examples to illustrate the results.