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Since February 2020, COVID-19 has spread rapidly to more than 200 countries in the world. During the pandemic, local governments in China have implemented different interventions to efficiently control the spread of the epidemic. Characterizing transmission of COVID-19 under some typical interventions is essential to help countries develop appropriate interventions. Based on the pre-symptomatic transmission patterns of COVID-19, we established a novel compartmental model: Susceptible-Infectious-Confirmed-Removed (SICR) model, which allowed the effective reproduction number to change over time, thus the effects of policies could be reasonably estimated. Using the epidemic data of Wuhan, Wenzhou, and Shenzhen, we migrated the corresponding estimated policy modes to South Korea, Italy, and the United States and simulated the potential outcomes for these countries when they adopted similar policy strategies to China. We found that the mild interventions implemented in Shenzhen were effective in controlling the epidemic in the early stage, while more stringent policies which were implemented in Wuhan and Wenzhou were necessary if the epidemic became severe and needed to be controlled in a short time. [ABSTRACT FROM AUTHOR]

This article considers a multi-period weighted mean-variance portfolio selection problem with uncertain time-horizon and a stochastic cash flow in a Markov regime-switching market. The random returns of risky assets and amount of the cash flow all depend on the states of a stochastic market which are assumed to follow a discrete-time Markov chain. Based on the conditional distribution of uncertain time-horizon caused by exogenous factors, we construct a more general mean-variance investment model. Within a game theoretic framework, we derive the equilibrium strategy and equilibrium value function in closed-form by applying backward induction approach. In addition, we show the equilibrium efficient frontier and discuss some degenerate cases. Finally, some numerical examples and sensitivity analysis are presented to illustrate equilibrium efficient frontiers and the effects of uncertain time-horizon on the equilibrium strategy and equilibrium efficient frontier as well as regime-switching and stochastic cash flow on the equilibrium efficient frontier. [ABSTRACT FROM AUTHOR]

This paper first studies the optimal reinsurance problems for two competitive insurers and then studies the optimal reinsurance premium pricing problem for their common reinsurer by using the dynamic programming technique. The two insurers are subject to common insurance systematic risk. Each purchases proportional or excess-of-loss reinsurance for risk control. They aim to maximize the expected utilities of their relative terminal wealth. With the insurers' optimal reinsurance strategies, the reinsurer decides the reinsurance premiums for each insurer, also aiming to maximize the expected utility of her terminal wealth. Thus, the optimal reinsurance pricing problem is formulated as a Stackelberg game between two competitive insurers and a reinsurer, where the reinsurer is the leader, and the insurers are followers. Besides, all three players take model ambiguity into account. We characterize the optimal strategies for the insurers and the reinsurer and provide some numerical examples to show the impact of competition and model ambiguity on the pricing of reinsurance contracts. [ABSTRACT FROM AUTHOR]

This paper investigates a robust optimal portfolio choice problem for a defined contribution (DC) pension plan member. The member worries about model ambiguity and aims to seek robust optimal investment strategies. Specifically, the member has a stochastic salary, considers inflation risk and invests her pension account wealth into a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock whose expected return rate follows a mean-reverting process. By using the dynamic programming approach, the robust optimal investment strategy and the corresponding value function are explicitly derived, and subsequently a verification theorem is provided. Furthermore, two special cases of our portfolio model are discussed. Finally, a numerical example is presented to reveal economic implications of our theoretical results and to illustrate the effects of the model parameters on the robust optimal investment strategy. We find that ambiguity about the dynamics of the inflation-indexed bond price and the stock price and expected return rate has different influences on the robust optimal investment strategy, and that neglecting ambiguity will always lead to utility loss. [ABSTRACT FROM AUTHOR]

In this paper, we present a computationally tractable optimization method for a robust mean-CVaR portfolio selection model under the condition of distribution ambiguity. We develop an extension that allows the model to capture a zero net adjustment via a linear constraint in the mean return, which can be cast as a tractable conic programme. Also, we adopt a nonparametric bootstrap approach to calibrate the levels of ambiguity and show that the portfolio strategies are relatively immune to variations in input values. Finally, we show that the resulting robust portfolio is very well diversified and superior to its non-robust counterpart in terms of portfolio stability, expected returns and turnover. The results of numerical experiments with simulated and real market data shed light on the established behaviour of our distributionally robust optimization model. [ABSTRACT FROM AUTHOR]

Chiu and Zhou [Quant. Finance, 2011,11, 115–123] show that the inclusion of a risk-free asset strictly boosts the Sharpe ratio in a continuous-time setting, which is in sharp contrast to the static single-period case. In this paper, we extend their work to a discrete-time setting. Specifically, we prove that the multi-period mean-variance efficient frontier generated by both risky and risk-free assets is strictly separated from that generated by only risky assets. As a result, we demonstrate that the inclusion of a risk-free asset strictly enhances the best Sharpe ratio of the efficient frontier in a multi-period discrete-time setting. Furthermore, we offer an explicit expression for the enhancement of the best Sharpe ratio, which was referred to as thepremium of dynamic tradingby Chiu and Zhou [op. cit.], although they do not present a computational formula for it. Our results further show that, in the case with a risk-free asset, if an investor can extract some money from his initial wealth at time 0, the efficient frontier with a risk-free asset can be tangent to that without a risk-free asset. Finally, based on real data from the American market, a numerical example is provided to illustrate the results obtained in this paper; a numerical comparison between the discrete-time case and the continuous-time case is also provided. Our numerical results reveal that the continuous-time model can be considered to be a limit of the discrete-time model. [ABSTRACT FROM AUTHOR]

In this paper, an ambiguity-averse insurer (AAI) whose surplus process is approximated by a Brownian motion with drift, hopes to manage risk by both investing in a Black–Scholes financial market and transferring some risk to a reinsurer, but worries about uncertainty in model parameters. She chooses to find investment and reinsurance strategies that are robust with respect to this uncertainty, and to optimize her decisions in a mean-variance framework. By the stochastic dynamic programming approach, we derive closed-form expressions for a robust optimal benchmark strategy and its corresponding value function, in the sense of viscosity solutions, which allows us to find a mean-variance efficient strategy and the efficient frontier. Furthermore, economic implications are analyzed via numerical examples. In particular, our conclusion in the mean-variance framework differs qualitatively, for certain parameter ranges, with model-uncertainty robustness conclusions in the framework of utility functions: model uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout and Liu. Our conclusion can be interpreted as saying that the mean-variance problem for the AAI explains certain counter-intuitive investor behaviors, by which the attitude to risk exposure, for an AAI facing model uncertainty, depends on positive past experience. [ABSTRACT FROM AUTHOR]

This article considers an investor who has an exogenous cash flow evolving according to a Lévy process and invests in a financial market consisting of only risky assets, whose prices are governed by exponential Lévy processes. Two continuous-time portfolio selection problems are studied for the investor. One is a benchmark problem, and the other is a mean-variance problem. The first problem is solved by adopting the stochastic dynamic programming approach, and the obtained results are extended to the second problem by employing the duality theory. Closed-form solutions of these two problems are derived. Some existing results are found to be special cases of our results. [ABSTRACT FROM PUBLISHER]