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Anomaly detection (AD) plays a vital role across a wide range of real-world domains by identifying data instances that deviate from expected patterns, potentially signaling critical events such as system failures, fraudulent activities, or…
Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be…
In this paper we propose a cyclical coordinate descent (CCD) algorithm for solving high dimensional risk parity problems. We show that this algorithm converges and is very fast even with large covariance matrices (n > 500). Comparison with…
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the…
Hedging methods to mitigate the exposure of variable annuity products to market risks require the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means these sensitivities…
Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…
Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how…
Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed…
This paper develops three polynomial-time pricing techniques for European Asian options with provably small errors, where the stock prices follow binomial trees or trees of higher-degree. The first technique is the first known Monte Carlo…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant…
Bayesian inference remains one of the most important tool-kits for any scientist, but increasingly expensive likelihood functions are required for ever-more complex experiments, raising the cost of generating a Monte Carlo sample of the…
Stochastic simulation techniques employed for the analysis of portfolios of insurance/reinsurance risk, often referred to as `Aggregate Risk Analysis', can benefit from exploiting state-of-the-art high-performance computing platforms. In…
The method and characteristics of several approaches to the pricing of discretely monitored arithmetic Asian options on stocks with discrete, absolute dividends are described. The contrast between method behaviors for options with an Asian…
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for…
In actuarial research, a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking, and capital…
Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in…
The value-at-risk of a delta-gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in…
In recommendation systems, items are likely to be exposed to various users and we would like to learn about the familiarity of a new user with an existing item. This can be formulated as an anomaly detection (AD) problem distinguishing…