Minimum Loss Probability Research Articles

Optimal liquidation with jump-diffusion process

Under the assumption of the asset prices obey jump-diffusion process, static optimal liquidation strategies and efficient frontier are provided based on the mean-variance criterion and the minimum loss probability criterion separately. Furthermore, this paper analysed the impact of price jump component on optimal liquidation strategy. And the results indicate that, under the mean-variance criterion, the price jump component will change the trajectory of the optimal liquidation strategy and the final liquidation cost. While under the minimum loss probability criterion, the price jump component will not affect the optimal liquidation strategy, but will change the value of minimum loss probability.

Optimal Liquidation Strategy of Multi-assets Based on Minimum Loss Probability

Based on the minimum loss probability criterion, this paper discusses the optimal strategy in multi-asset liquidation. First, we give the framework of the multi-asset liquidation problem and obtain the boundary conditions of the optimal liquidation strategy under the assumption of linear price impact functions and transform the multi-asset liquidation problem into the portfolio liquidation problem. On this basis, the asymptotic solution and numerical solution of the optimal liquidation strategy are obtained. Then, we simulate the trajectories of the optimal liquidation strategy and analyze the effects of parameters changes.

The M/D/1+D queue has the minimum loss probability among M/G/1+G queues

We consider the loss probability Ploss in the stationary M/G/1 queue with generally distributed impatience times (M/G/1+G queue). Recently, it was shown that Ploss increases with service times in the convex order. In this paper, we show that Ploss also increases with impatience times in the excess wealth order. With these results, we show that Ploss in the M/D/1+D queue is smallest among all M/G/1+G queues with the same and finite arrival rate, mean service time, and mean impatience time.

A tandem network with a sharing buffer

In this paper, we consider a two-stage tandem network. The customers waiting in these two stages share one finite buffer. By constructing a Markov process, we derive the stationary probability distribution of the system and the sojourn time distribution. Given some constraints on the minimum loss probability and the maximum waiting time, we also derive the optimal buffer size and the shared-buffer size by minimizing the total buffer costs. Numerical results show that, by adopting the buffer-sharing policy, the customer acceptance fraction and the delivery reliability are more sensitive to buffer size comparing with the buffer-allocation policy.