Related papers: Risk-neutral pricing for APT
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets…
We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the…
We study super--replication of European contingent claims in an illiquid market with insider information. Illiquidity is captured by quadratic transaction costs and insider information is modeled by an investor who can peek into the future.…
We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is…
In this paper, we derive a temporal arbitrage policy for storage via reinforcement learning. Real-time price arbitrage is an important source of revenue for storage units, but designing good strategies have proven to be difficult because of…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
We study an online dynamic pricing problem where the potential demand at each time period $t=1,2,\ldots, T$ is stochastic and dependent on the price. However, a perishable inventory is imposed at the beginning of each time $t$, censoring…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
We propose a Fundamental Theorem of Asset Pricing and a Super-Replication Theorem in a model-independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as…
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 literature for a dual risk…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the…
This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…
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…
This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete. the…
The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The…
We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively…
In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…