Bensoussan, Alain
https://hdl.handle.net/10735.1/3180
2020-07-13T12:47:33Z
2020-07-13T12:47:33Z
A Paradox in Time-Consistency in the Mean-Variance Problem?
Bensoussan, Alain
Wong, Kwok Chuen
Yam, Sheung Chi Phillip
https://hdl.handle.net/10735.1/7952
2020-04-15T08:01:18Z
2018-12-19T00:00:00Z
A Paradox in Time-Consistency in the Mean-Variance Problem?
Bensoussan, Alain; Wong, Kwok Chuen; Yam, Sheung Chi Phillip
We establish new conditions under which a constrained (no short-selling) time-consistent equilibrium strategy, starting at a certain time, will beat the unconstrained counterpart, as measured by the magnitude of their corresponding equilibrium mean-variance value functions. We further show that the pure strategy of solely investing in a risk-free bond can sometimes simultaneously dominate both constrained and unconstrained equilibrium strategies. With numerical experiments, we also illustrate that the constrained strategy can dominate the unconstrained one for most of the commencement dates (even more than 90%) of a prescribed planning horizon. Under a precommitment approach, the value function of an investor increases with the size of the admissible sets of strategies. However, this may fail to be true under the game-theoretic paradigm, as the constraint of time-consistency itself affects the value function differently when short-selling is and is not prohibited.
Due to copyright restrictions and/or publisher's policy full text access from Treasures at UT Dallas is limited to current UTD affiliates (use the provided Link to Article).
2018-12-19T00:00:00Z
Joint Inventory-Pricing Optimization with General Demands: An Alternative Approach for Concavity Preservation
Bensoussan, Alain
Xie, Y.
Yan, H.
https://hdl.handle.net/10735.1/7935
2020-04-14T08:01:02Z
2019-05-23T00:00:00Z
Joint Inventory-Pricing Optimization with General Demands: An Alternative Approach for Concavity Preservation
Bensoussan, Alain; Xie, Y.; Yan, H.
In this study, we provide an alternative approach for proving the preservation of concavity together with submodularity, and apply it to finite-horizon non-stationary joint inventory-pricing models with general demands. The approach characterizes the optimal price as a function of the inventory level. Further, it employs the Cauchy–Schwarz and arithmetic-geometric mean inequalities to establish a relation between the one-period profit and the profit-to-go function in a dynamic programming setting. With this relation, we demonstrate that the one-dimensional concavity of the price-optimized profit function is preserved as a whole, instead of separately determining the (two-dimensional) joint concavities in price (or mean demand/risk level) and inventory level for the one-period profit and the profit-to-go function in conventional approaches. As a result, we derive the optimality condition for a base-stock, list-price (BSLP) policy for joint inventory-pricing optimization models with general form demand and profit functions. With examples, we extend the optimality of a BSLP policy to cases with non-concave revenue functions in mean demand. We also propose the notion of price elasticity of the slope (PES) and articulate the condition as that in response to a price change of the commodity, the percentage change in the slope of the expected sales is greater than the percentage change in the slope of the expected one-period profit. The concavity preservation conditions for the additive, generalized additive, and location-scale demand models in the literature are unified under this framework. We also obtain the conditions under which a BSLP policy is optimal for the logarithmic and exponential form demand models. © 2019 Production and Operations Management Society
2019-05-23T00:00:00Z
A Mean-Variance Approach to Capital Investment Optimization
Bensoussan, Alain
Hoe, S.
Yan, Z.
https://hdl.handle.net/10735.1/7057
2019-11-01T08:01:12Z
A Mean-Variance Approach to Capital Investment Optimization
Bensoussan, Alain; Hoe, S.; Yan, Z.
We develop an improved model of capital investment under uncertainty that incorporates the variance of the capital stock in the payoff functional to manage risk. Our model results in a mean field type control problem that cannot be solved by classical stochastic control methods. We solve our problem using techniques presented in Bensoussan, Frehse, and Yam [Mean Field Games and Mean Field Type Control Theory, Springer, New York, 2013]. The explicit solution is a feedback depending on the initial condition. Moreover, our model can be reduced to Abel's [Amer. Econ. Rev., 73 (1983), pp. 228-233]. Numerical results suggest that the risk reduction optimally exceeds the cost incurred. Following Björk, Khapko, and Murgoci [Finance Stoch., 21 (2017), pp. 331-360], we solve for a time-consistent solution, i.e., the best possible feedback independent of the initial condition. The time-consistent policy discards our risk specification, with the resultant loss of value to the firm. © 2019 Society for Industrial and Applied Mathematics
Full text access from Treasures at UT Dallas is restricted to current UTD affiliates (use the provided Link to Article).
The Impact of Competitive Advantage on the Investment Timing in Stackelberg Leader–Follower Game
Hoe, S.
Yan, Z.
Bensoussan, Alain
https://hdl.handle.net/10735.1/6818
2019-08-31T08:01:10Z
The Impact of Competitive Advantage on the Investment Timing in Stackelberg Leader–Follower Game
Hoe, S.; Yan, Z.; Bensoussan, Alain
This short note clarifies how the Stackelberg leader’s competitive advantage after the follower’s entry affects the leader’s optimal market entry decision and Stackelberg strategic interactions under uncertainty. Although the Stackelberg leader’s first investment threshold remains constant and coincides with the monopolist’s investment trigger, his second (third) investment threshold, which defines the exit (entry) of the first (second) investment interval, increases with an increased competitive advantage. With an increased competitive advantage, the probability of sequential investment equilibrium (simultaneous investment equilibrium) increases (decreases) irrespective of the level of volatility. Moreover, for a given level of competitive advantage, an increase in the volatility tends to decrease (increase) the probability of simultaneous investment equilibrium (sequential investment equilibrium). For a richer set of results, endogenous firm roles are examined and analyzed as well. The leader’s preemptive threshold is negatively affected by his competitive advantage.
Full text access from Treasures at UT Dallas is restricted to current UTD affiliates (use the provided Link to Article).