Related papers: Time-Consistent Actuarial Valuations
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…
Statistical arbitrage exploits temporal price differences between similar assets. We develop a unifying conceptual framework for statistical arbitrage and a novel data driven solution. First, we construct arbitrage portfolios of similar…
This paper is concerned with a time-inconsistent recursive stochastic control problems where the forward state process is constrained through an additional recursive utility system. By adapting the Ekeland variational principle, necessary…
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…
We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…
Continuous time financial market models are often motivated as scaling limits of discrete time models. The objective of this paper is to establish such a connection for a robust framework. More specifically, we consider discrete time models…
People often face trade-offs between costs and benefits occurring at various points in time. The predominant discounting approach is to use the exponential form. Central to this approach is the discount rate, a unique parameter that…
Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct…
In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study…
We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple-prior optimal stopping we propose a valuation functional with sound…
Price-based revenue management is an important problem in operations management with many practical applications. The problem considers a retailer who sells a product (or multiple products) over $T$ consecutive time periods and is subject…
The law of one price (LOP) broadly asserts that identical financial flows should command the same price. We show that, when properly formulated, LOP is the minimal condition for a well-defined mean-variance portfolio selection framework…
Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual…
Auction is applied for trade with various mechanisms. A simple but practical question is which mechanism, typically first-price or second-price auctions, is preferred from the perspective of bidders or sellers. A celebrated answer is…
We study the problem of designing posted-price mechanisms in order to sell a single unit of a single item within a finite period of time. Motivated by real-world problems, such as, e.g., long-term rental of rooms and apartments, we assume…
We provide an axiomatic approach to general premium principles in a probability-free setting that allows for Knightian uncertainty. Every premium principle is the sum of a risk measure, as a generalization of the expected value, and a…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly…