arXiv research

Derives explicit investment strategy with random endowment.

In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization problem not only the initial capital but also the number of units of the random end…

New method for dynamic valuation in markets with random endowments.

We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that both primal and dual value functions are finite in the interiors of their domains a…

In this paper we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on t…

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 defined via the consistent price system (CPS) such that the liquidation value p…

In this paper, we consider a numéraire-based utility maximization problem under constant proportional transaction costs and random endowment. Assuming that the agent cannot short sell assets and is endowed with a strictly positive contingent claim, a primal optimizer of this utility maximization problem exists. Moreove…

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility maximization problems including the classical one…

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical one…

We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…

We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization allows us to derive the monotonicity and concavity of the optimal consumption as a…

We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjec…

This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset framework with a cash account. At the terminal time T, the investor can receive unb…

We consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions f…

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies -- t…

We treat utility maximization from terminal wealth for an agent with utility function $U:\mathbb{R}\to\mathbb{R}$ who dynamically invests in a continuous-time financial market and receives a possibly unbounded random endowment. We prove the existence of an optimal investment without introducing the associated dual prob…

Study shows mass distribution of random holomorphic sections follows a central limit theorem.

We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options. We show …

We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of asymptotic elasticity of Kramkov and Schachermayer is ext…

The study finds arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps.

Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with the representation. Working towards operational representation learning, we endow…

We study the set of marginal utility-based prices of a financial derivative in the case where the investor has a non-replicable random endowment. We provide an example showing that even in the simplest of settings - such as Samuelson's geometric Brownian motion model - the interval of marginal utility-based prices can …

A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and othe…

We review the utility-based valuation method for pricing derivative securities in incomplete markets. In particular, we review the practical approach to the utility-based pricing by the means of computing the first order expansion of marginal utility-based prices with respect to a small number of random endowments.

We consider a power utility maximization problem with additive habits in a framework of discrete-time markets and random endowments. For certain classes of incomplete markets, we establish estimates for the optimal consumption stream in terms of the aggregate state price density, investigate the asymptotic behaviour of…

The length of shortest non-simple geodesics grows logarithmically with surface genus.

Covariance is shown as a commutator in random variable calculus.

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 framework, we extend our analysis to the more challenging unbounded case. Our methodolo…

The sectional curvature of a compact Riemannian manifold M can be seen as a random variable on the Grassmann bundle of 2-planes in TM endowed with the Fubini-Study volume density. In this article we calculate the moments of this random variable by integrating suitable local Riemannian invariants and discuss the distrib…

We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We show with ex…

Estimates metric tensor on neuromanifolds using Fisher information and random methods.

An investor with constant absolute risk aversion trades a risky asset with general Itô-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless op…

In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop equilibrium consumption-investment pair in terms of a coupled forward-backward …

Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal constraints.We deal with random endowment density streams which admit jumps and g…

Monotone aggregation of dependent random vectors has an absolutely continuous distribution under certain conditions.

In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the numéraire-based model and work with utility functions only supporting R+. Under the assumption of existence of consistent price sy…

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward …

Random scan CAVI converges linearly under log-concave assumptions.

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the shortfall minimization p…

Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the volatility of asset prices (as well as the drift) varies. Degeneracies arise from …

Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the related variational problems and optimization problems. Random convex analysis is …

Study of random sections on complex spaces converging to equilibrium metrics.

In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach is based on a general representation result for monotone convex functionals, a fu…

We consider a point cloud $X_n := \{ x_1, \dots, x_n \}$ uniformly distributed on the flat torus $\mathbb{T}^d : = \mathbb{R}^d / \mathbb{Z}^d$, and construct a geometric graph on the cloud by connecting points that are within distance $\varepsilon$ of each other. We let $\mathcal{P}(X_n)$ be the space of probability …

In this paper we ask whether, given a stock market and an illiquid derivative, there exists arbitrage-free prices at which an utility-maximizing agent would always want to buy the derivative, irrespectively of his own initial endowment of derivatives and cash. We prove that this is false for any given investor if one c…

The paper analyzes Random Search and introduces BLiN-MOS for bandit learning.

The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent's set of st…

New method speeds up optimization over probability measures.