Related papers: Optimal Portfolio under Fractional Stochastic Envi…
In this paper, we construct a solution to the optimal contract problem for delegated portfolio management of the fist-best (risk-sharing) type. The novelty of our result is (i) in the robustness of the optimal contract with respect to…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
The financial model proposed involves the liquidation process of a portfolio of $n$ assets through sell or (and) buy orders with volatility. We present the rigorous mathematical formulation of this model in a financial setting resulting to…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also…
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both…
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward…
We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…
This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our…
We study the problem of dynamically trading multiple futures whose underlying asset price follows a multiscale central tendency Ornstein-Uhlenbeck (MCTOU) model. Under this model, we derive the closed-form no-arbitrage prices for the…
We study option prices in financial markets where the risky asset prices are modelled by jump diffusions. It was proposed by Schweizer (1996) in a general semimartingale setting, following earlier works by F\"ollmer and Sondermann (1986)…
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…
The classical Merton investment problem predicts deterministic, state-dependent portfolio rules; however, laboratory and field evidence suggests that individuals often prefer randomized decisions leading to stochastic and noisy choices.…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz' mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to…
We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require…
This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a…
In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered…
Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize…