arXiv subjects

Masashi Ieda

Publications and source records attributed to Masashi Ieda.

4 recordsLinked to original sources

arXiv2022

Continuous-time Portfolio Optimization for Absolute Return Funds

This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance criterion based on the lower mean square error between the investor's wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton-Jacobi-Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper.

q-fin.PM↗

arXiv2015

A dynamic optimal execution strategy under stochastic price recovery

In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order, which is defined as a Cox process whose intensity increases by the degree of the market impact. We include not only the market order but also the limit order in our strategy in a restricted fashion. We formulate the problem as a combined stochastic control problem over a finite time horizon. The corresponding Hamilton-Jacobi-Bellman quasi-variational inequality is solved numerically. The optimal strategy obtained consists of three components: (i) the initial large trade; (ii) the unscheduled small trades during the period; (iii) the terminal large trade. The size and timing of the trade is governed by the tolerance for market impact depending on the state at each time step, and hence the strategy behaves dynamically. We also provide competitive results due to inclusion of the limit order, even though a limit order is allowed under conservative evaluation of the execution price.

q-fin.TR↗

arXiv2013

An implicit method for the finite time horizon Hamilton-Jacobi-Bellman quasi-variational inequalities

We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an implicit method in the field of numerical methods for partial differential equations, and thus it is advantageous in the sense that the stability condition is independent of the discretization parameters. We apply our method to the finite time horizon optimal forest harvesting problem, which considers exiting from the forestry business at a finite time. We show that the behavior of the obtained optimal harvesting strategy of the extended problem coincides with our intuition.

math.NA↗

arXiv2013

A liability tracking approach to long term management of pension funds

We propose a long term portfolio management method which takes into account a liability. Our approach is based on the LQG (Linear, Quadratic cost, Gaussian) control problem framework and then the optimal portfolio strategy hedges the liability by directly tracking a benchmark process which represents the liability. Two numerical results using empirical data published by Japanese organizations are served: simulations tracking an artificial liability and an estimated liability of Japanese organization. The latter one demonstrates that our optimal portfolio strategy can hedge his or her liability.

q-fin.PM↗