Related papers: Good deal bounds with convex constraints
We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising…
The convexity of a set can be generalized to the two weaker notions of reach and $r$-convexity; both describe the regularity of a set's boundary. For any compact subset of $\mathbb{R}^d$, we provide methods for computing upper bounds on…
Dynamic spectral risk measures define a claim's valuation bounds as supremum and infimum of expectations of the claim's payoff over a dominated set of measures. The measures at which such extrema are attained are called extreme measures. We…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…
This paper examines replication portfolio construction in incomplete markets - a key problem in financial engineering with applications in pricing, hedging, balance sheet management, and energy storage planning. We model this as a…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
The system operator's scheduling problem in electricity markets, called unit commitment, is a non-convex mixed-integer program. The optimal value function is non-convex, preventing the application of traditional marginal pricing theory to…
We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the…
We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
In the context of dealing with financial risk management problems it is desirable to have accurate bounds for option prices in situations when pricing formulae do not exist in the closed form. A unified approach for obtaining upper and…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…
We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where…
We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly…
We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for…
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…