Related papers: Shadow price in the power utility case
We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for…
Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…
We consider the discretized Bachelier model where hedging is done on an equidistant set of times. Exponential utility indifference prices are studied for path-dependent European options and we compute their non-trivial scaling limit for a…
G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…
Optimizing the total cost of power systems is a common tool for network operation and planning. Besides valuable information about how to run and possibly expand a power system, the optimization provides an optimal Locational Marginal Price…
In the large financial market, which is described by a model with countably many traded assets, we formulate the problem of the expected utility maximization. Assuming that the preferences of an economic agent are modeled with a stochastic…
We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the prices of generating fuels into electricity…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
We analyze the efficiency of markets with friction, particularly power markets. We model the market as a dynamic system with $(d_t;\,t\geq 0)$ the demand process and $(s_t;\,t\geq 0)$ the supply process. Using stochastic differential…
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 determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called {\it probability of drawdown}, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its…
We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference…
Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this…
Pricing schemes are an important smart grid feature to affect typical energy usage behavior of energy users (EUs). However, most existing schemes use the assumption that a buyer pays the same price per unit of energy to all suppliers at any…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
With the increasing use of auctions in online advertising, there has been a large effort to study seller revenue maximization, following Myerson's seminal work, both theoretically and practically. We take the point of view of the buyer in…
Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…