Related papers: Optimal measure preserving derivatives revisited
This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal the expectation constraint, an auxiliary stochastic control problem is firstly solved by two new…
This paper investigates arbitrage properties of financial markets under distributional uncertainty using Wasserstein distance as the ambiguity measure. The weak and strong forms of the classical arbitrage conditions are considered. A…
Many investment models in discrete or continuous-time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original…
In this paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting. This gives rise to time-inconsistency of the decision-maker. If the decision-maker at time t=0 can commit his/her…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
This tutorial describes recently developed general optimality conditions for Markov Decision Processes that have significant applications to inventory control. In particular, these conditions imply the validity of optimality equations and…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…
This paper studies the utility maximization on the terminal wealth with random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios…
It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous-time Markovian context. This holds true in market models where no…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
In commodity markets the convergence of futures towards spot prices, at the expiration of the contract, is usually justified by no-arbitrage arguments. In this article, we propose an alternative approach that relies on the expected profit…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We define two…
We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the…
This paper studies the market phenomenon of non-convergence between futures and spot prices in the grains market. We postulate that the positive basis observed at maturity stems from the futures holder's timing options to exercise the…
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…
We use the martingale method to discuss the relationship between mean-variance (MV) and monotone mean-variance (MMV) portfolio selections. We propose a unified framework to discuss the relationship in general financial markets without any…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not…