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The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation…
This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded…
A price-maker company extracts an exhaustible commodity from a reservoir, and sells it instantaneously in the spot market. In absence of any actions of the company, the commodity's spot price evolves either as a drifted Brownian motion or…
We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and the shape of the LOB. We present an empirical analysis showing that the type of the last order significantly alters the…
We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that…
We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling…
We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures…
We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption…
We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval…
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly…
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment…
We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the…
We introduce an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the…
In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates the risky investment, consumption and leisure rate to maximise a gain function characterised by a power utility function of consumption…
In the present paper, we investigate the optimal capital injection behaviour of an insurance company if the interest rate is allowed to become negative. The surplus process of the considered insurance entity is assumed to follow a Brownian…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a…
This paper investigates the optimal investment, consumption, and life insurance strategies for households under the impact of health shock risk. Considering the uncertainty of the future health status of family members, a non-homogeneous…
In this paper, we describe a novel agent-based approach for modelling the transaction cost of buying or selling an asset in financial markets, e.g., to liquidate a large position as a result of a margin call to meet financial obligations.…