An Optimal Dividend Problem with Capital Injections over a Finite Horizon
In this paper we propose and solve an optimal dividend problem with capital injections over a finite time horizon. The surplus dynamics obeys a linearly controlled drifted Brownian motion that is reflected at the origin, dividends give rise to time-dependent instantaneous marginal profits, whereas capital injections are subject to time-dependent instantaneous marginal costs. The aim is to maximize the sum of a liquidation value at terminal time and of the total expected profits from dividends, net of the total expected costs for capital injections. Inspired by the study of El Karoui and Karatzas (1989) on reflected follower problems, we relate the optimal dividend problem with capital injections to an optimal stopping problem for a drifted Brownian motion that is absorbed at the origin. We show that whenever the optimal stopping rule is triggered by a time-dependent boundary, the value function of the optimal stopping problem gives the derivative of the value function of the optimal dividend problem. Moreover, the optimal dividend strategy is also triggered by the moving boundary of the associated stopping problem. The properties of this boundary are then investigated in a case study in which instantaneous marginal profits and costs from dividends and capital injections are constants discounted at a constant rate.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
On the closed-form expected NPVs of double barrier strategies for regular diffusions
The core of the research is to provide the explicit expression for the expected net present values (NPVs) of double barrier strategies for regular diffusions on the real line without solving differential equations. Under…
FormEquilibrium Policy on Dividend and Capital Injection under Time-inconsistent Preferences
This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-cons…
Asymptotic Analysis for Optimal Dividends in a Dual Risk Model
The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literatur…
A Note on the Optimal Dividends Paid in a Foreign Currency
We consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted …
Asset Prices with Overlapping Generations and Capital Accumulation: Tirole (1985) Revisited
We revisit the classic paper of Tirole "Asset Bubbles and Overlapping Generations" (1985, Econometrica), which shows that the emergence of asset bubbles solves the capital over-accumulation problem. While Tirole's main i…