A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method uses PINNs to efficiently compute Gerber-Shiu functions.
In this paper we revisit the method of off-policy corrections for reinforcement learning (COP-TD) pioneered by Hallak et al. (2017). Under this method, online updates to the value function are reweighted to avoid divergence issues typical of off-policy learning. While Hallak et al.'s solution is appealing, it cannot ea…
This paper considers an insurance surplus process modeled by a spectrally negative Lévy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the joint distribution of the time of drawdown, the running maximum at drawdown, the last m…
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations satisfied by the Gerber-Shiu f…
A new algorithm finds optimal solutions for constrained decision processes.
We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability a…
Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of opti…
This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative Lévy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The objective is to maximize the sum of …
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differ…
Review of Gerber-Shiu function for practical actuarial science.
This paper studies the risk-adjusted optimal timing to liquidate an option at the prevailing market price. In addition to maximizing the expected discounted return from option sale, we incorporate a path-dependent risk penalty based on shortfall or quadratic variation of the option price up to the liquidation time. We …
Study optimal portfolio strategies with time-varying discount rates.
This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov processes. The control mechanism chooses the size of dividend payments. The obje…
New RL approach handles non-exponential discounting for sequential decisions.
Reinforcement learning (RL) typically defines a discount factor as part of the Markov Decision Process. The discount factor values future rewards by an exponential scheme that leads to theoretical convergence guarantees of the Bellman equation. However, evidence from psychology, economics and neuroscience suggests that…
In this paper, we study the dividend strategies for a shareholder with non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to the Markov strategies. This is a time inconsistent control problem. The extended HJB equation is given an…
Study optimal stopping for group with diverse discount rates using an attitude function.
We study the problem of learning policy of an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle from a given mixture policy class characterized by the convex hull of a set of k…
Investment decisions shift earlier as patience decreases, with implications for pasting conditions.
The paper analyzes optimal dividend and capital injection strategies under time-inconsistent preferences.
We optimize discounts to maximize influence spread in social networks.
Study analyzes household capital risk and poverty trapping, deriving a new function for capital deficit distribution.
Intertemporal decision making involves choices among options whose effects occur at different moments. These choices are influenced not only by the effect of rewards value perception at different moments, but also by the time perception effect. One of the main difficulties that affect standard experiments involving int…
This paper presents an algorithm for pricing perpetual American put options with asset-dependent discounting.
We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a smooth classical solution to the corresponding HJB equation. Moreover, some verif…
The study uses reproducing kernels to model bond discount curves.
New offline RL method handles average-reward MDPs with single-policy coverage.
New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
New RL difficulty shown for discounted settings.
A central problem in ranking is to design a ranking measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the widely used Normalized Discounted Cumulative Gain (NDCG)-type ranking measures. Although there are extensive empirical studies of NDCG, little is known about its t…
Global minima found for multidimensional scaling with penalties.
In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representative investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switches…
The paper analyzes perpetual American options with asset-dependent discounting.
New algorithm reduces online regression error in RKHS.
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
Lower discount factors act as a regularizer in RL, improving performance.
In this paper, we introduce a novel combined reward cum penalty loss function to handle the regression problem. The proposed combined reward cum penalty loss function penalizes the data points which lie outside the -tube of the regressor and also assigns reward for the data points which lie inside of the -tube of…
The paper studies robust risk measures with linear penalties under uncertain distributions.
In the spirit of [Surya07'], we develop an average problem approach to prove the optimality of threshold type strategies for optimal stopping of Lévy models with a continuous additive functional (CAF) discounting. Under spectrally negative models, we specialize this in terms of conditions on the reward function and ran…
Curvature penalties improve interpretability of KANs without sacrificing accuracy.
N-discount optimality was introduced as a hierarchical form of policy- and value-function optimality, with Blackwell optimality lying at the top level of the hierarchy Veinott (1969); Blackwell (1962). We formalize notions of myopic discount factors, value functions and policies in terms of Blackwell optimality in MDPs…
We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the demand of the insider and the price functions are in general non-linear and remai…
Paper tackles time inconsistency in portfolio management with stochastic volatility and power utility.
In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a -distance function and …
New theory extends LQ control to non-exponential discount scenarios.
A firm with heterogeneous shareholders optimizes dividends under ambiguity aggregation.
The policy gradient theorem describes the gradient of the expected discounted return with respect to an agent's policy parameters. However, most policy gradient methods drop the discount factor from the state distribution and therefore do not optimize the discounted objective. What do they optimize instead? This has be…
We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spendings/dividend payments, given that the discounting factor is given by an exponential CIR process. In the d…