We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A …
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48 results for “discounting sensitivities”
Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.
problem Optimizing decision-making under risk in Markov processes.
method Analyzes risk-sensitive criteria using Optimized Certainty Equivalent, including entropic risk and Conditional Value-at-Risk.
result Conditions for the existence of optimal policies and solution procedures are provided.
We introduce a general framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and behavioral economics. Within the framework, applying weighted norm spaces to incorporate …
We show that different rates should be used for borrowing and discount rates, and that the risk-free rate should be used for discounting when assessing and comparing the cost of energy accross diffferent producers and technologies, on the example of photovoltaics. Recent quantitative models using the same rate for borr…
Study cash-flow forecasting for derivatives, aligning with replication strategy and addressing timing frictions.
problem Inconsistencies in cash-flow forecasting under different measures and stochastic payment times.
method Use discounting sensitivities (funding-curve hedge ratios) for replication and propose a liquidity valuation adjustment.
result Aligns forecasting with replication strategy and avoids measure-mixing issues.
This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optim…
Study risk-sensitive reinforcement learning with entropic risk measures and generative models.
problem Risk-sensitive reinforcement learning in discounted MDPs with recursive entropic risk measures.
method Introduced Model-Based ERM -Value Iteration (MB-RS-QVI) and derived PAC bounds on sample complexity for value and policy learning.
result PAC bounds show exponential dependence on , with tight bounds in and .
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such c…
Study optimal stopping for group with diverse discount rates using an attitude function.
problem Optimal stopping for a group with diverse discount rates under an aggregation preference.
method Develop iterative approach using consistent planning for time-consistent equilibria.
result Characterize all time-consistent mild equilibria as fixed points of an operator.
On the Sample Complexity of Discounted Reinforcement Learning with Optimized Certainty Equivalentscs.LG
Study risk-sensitive reinforcement learning with optimized certainty equivalents.
problem Risk-sensitive reinforcement learning in finite discounted MDPs.
method Analyzed a simple model-based approach and derived PAC sample complexity bounds.
result Established tight sample complexity bounds for value and policy learning.
Develops an actor-critic algorithm for risk-sensitive Markov decision processes.
problem Risk-sensitive cost criterion in Markov decision processes.
method Actor-critic algorithm with function approximation.
result Asymptotic convergence of the actor-critic algorithm.
For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount rate and has generated …
We present a framework on how to hedge the interest rate sensitivity of liabilities discounted by an extrapolated yield curve. The framework is based on functional analysis in that we consider the extrapolated yield curve as a functional of an observed yield curve and use its Gâteaux variation to understand the sensiti…
This paper analyzes risk-sensitive reinforcement learning with Conditional Value-at-Risk (CVaR) for robust Markov Decision Processes.
problem Risk-sensitive reinforcement learning for robust Markov Decision Processes (RMDPs) with state-action-dependent ambiguity sets.
method The paper establishes a connection between robustness and risk sensitivity, defining a new risk measure NCVaR and proposing value iteration algorithms.
result The proposed approach using NCVaR optimization and value iteration algorithms can solve problems with state-action-dependent ambiguity sets.
This study prioritizes temporal resolution over spatial in energy systems models due to higher influence.
problem The impact of spatial and temporal resolution on energy system models.
method Global sensitivity analysis to compare structural aspects, spatial, and temporal resolution.
result Temporal resolution has a higher influence on all results parameters compared to spatial resolution.
This paper proposes a method for estimating consumer preferences among discrete choices, where the consumer chooses at most one product in a category, but selects from multiple categories in parallel. The consumer's utility is additive in the different categories. Her preferences about product attributes as well as her…
In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company that controls risk exposure by purchasing proportional reinsurance. We assume the preference of the insurer is of CRRA form. By solving the corresponding Hamilton-Jacobi-Bellman equation, w…
Paper develops a discounted algorithm for online convex optimization that adapts to unknown discount factors.
problem Developing an algorithm that can adapt to an unknown discount factor in online convex optimization.
method Smoothed Online Gradient Descent (SOGD) with Discounted-Normal-Predictor (DNP).
result Achieves a uniform discounted regret across a continuous interval of discount factors.
We consider a simple investment project with the following parameters: I>0: Initial investment which is amortizable in n years; n: Number of years the investment allows production with constant output per year; A>0: Annual amortization (A=I/n); Q>0: Quantity of products sold per year; Cv>0: Variable cost per unit; p>0:…
Paper introduces non-linear discounting models for default compensation and climate valuation.
problem Valuation of non-replicable value and damage under default risk.
method Develops two models: one for risk-neutralising discounting and another for survival probability dependent discounting.
result Non-decaying discount factors (negative discount rates) are possible under certain scenarios.
The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of consumption at any given time depends only on the amount consumed at that time.…
Dynamic Network Riskq-fin.GN
The paper finds stocks with higher dynamic network risk have lower returns.
problem Understanding and pricing short-term and long-term dynamic network risk in stock returns.
method Examined the relationship between stock sensitivities to dynamic network risk and expected returns, using economic theory and empirical analysis.
result A one-standard deviation increase in long-term network risk loadings associates with a 7.66% drop in annualized expected returns.
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a deterministic function of the…
Study analyzes how discounts affect train ticket purchases and rescheduling in Switzerland.
problem Understanding how discounts influence train ticket buying and rescheduling behavior.
method Machine learning techniques, including causal machine learning, to analyze survey data.
result Increasing a discount rate by 1% increases the rescheduled trip share by 0.16% among always buyers.
Proves lower discount rates are needed for future losses.
problem Determining appropriate discount rates for future losses.
method Analyzes climate change and discount rates debate.
result Risk requires a lower, not higher, discount rate.
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…
Repo convexityq-fin.PR
There is an observed basis between repo discounting, implied from market repo rates, and bond discounting, stripped from the market prices of the underlying bonds. Here, this basis is explained as a convexity effect arising from the decorrelation between the discount rates for derivatives and bonds. Using a Hull-White …
Discount Modelsq-fin.MF
Proposes a new framework for discount models.
problem Arbitrage-free dynamic framework for discount models.
method Derives general consistency conditions for factor models.
result Alternative to Heath--Jarrow--Morton framework for forward rates.
In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particular we consider credit-risky assets that may include random recovery upon default. The market filtration is generated by a collection of information processes associated with economic…
This paper shows how forward rate interpolations are equivalent to discount factor interpolations in yield curve construction.
problem The challenge of choosing between different interpolation methods for yield curve construction.
method Demonstrates the equivalence between forward rate interpolations and discount factor interpolations.
result Some popular interpolation methods on forward rates are equivalent to classical interpolation methods on discount factors.
The objective in a traditional reinforcement learning (RL) problem is to find a policy that optimizes the expected value of a performance metric such as the infinite-horizon cumulative discounted or long-run average cost/reward. In practice, optimizing the expected value alone may not be satisfactory, in that it may be…
New RL approach handles non-exponential discounting for sequential decisions.
problem Modeling human discounting in sequential decision-making tasks.
method Generalized model-based reinforcement learning with arbitrary discount functions, using Hamilton-Jacobi-Bellman equation and collocation method.
result Validated approach on simulated problems, showing applicability to human discounting.
Stochastic discount factorsq-fin.PR
The valuation process that economic agents undergo for investments with uncertain payoff typically depends on their statistical views on possible future outcomes, their attitudes toward risk, and, of course, the payoff structure itself. Yields vary across different investment opportunities and their interrelations are …
We optimize discounts to maximize influence spread in social networks.
problem Maximizing influence spread in social networks with fractional discounts.
method Developed an efficient (1-1/e)-approximation algorithm for NP-hard problem.
result Achieved an approximation of 1-1/e for influence maximization.
Study optimal portfolio strategies with time-varying discount rates.
problem Optimizing portfolio decisions with a non-constant discount rate.
method Introduced subgame perfect strategies to handle time inconsistency, using fixed point iteration to find the utility-weighted discount rate.
result Subgame perfect strategies are equivalent to optimal strategies under certain utility function assumptions.
The study uses reproducing kernels to model bond discount curves.
problem Estimating bond discount curves under no-arbitrage conditions.
method Introduced reproducing kernels as a regression basis for estimating bond discount curves.
result Reproducing kernels provide a tractable solution for calibrating models to market data.
We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpreta- tions for three models of demand (arithmetic Brownian, geometric Brownian…
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…
New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
problem Discount regularization leads to poor performance in unevenly sampled data.
method Equivalence theorem showing discount regularization as a strong prior, setting regularization parameters locally for individual state-action pairs.
result Discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
New RL difficulty shown for discounted settings.
problem Difficulty in reinforcement learning with discounted rewards.
method Adapted Wang et al. (2020) construction to 2-state MDP.
result Learning impossible even with infinite data in discounted setting.
UCBVI-γ algorithm minimizes regret in discounted MDPs.
problem Minimizing regret in discounted MDPs.
method Optimism in the face of uncertainty principle and Bernstein-type bonus.
result UCBVI-γ achieves nearly minimax optimal regret.
The policy gradient theorem is defined based on an objective with respect to the initial distribution over states. In the discounted case, this results in policies that are optimal for one distribution over initial states, but may not be uniformly optimal for others, no matter where the agent starts from. Furthermore, …
Lower discount factors act as a regularizer in RL, improving performance.
problem Improving RL performance with limited data.
method Explicitly equating reduced discount factors to regularization terms.
result Regularization effectiveness depends on data properties.
Derivative pricing is about cash flow discounting at the riskfree rate. This teaching has lost its meaning post the financial crisis, due to the addition of extra value adjustments (XVA), which also made derivatives pricing and valuation a very difficult task for investors. This article recovers a properly defined disc…
A new algorithm finds optimal solutions for constrained decision processes.
problem Optimizing state-value functions with constraints in CMDPs.
method Gradient-Aware Search (GAS) exploiting PWLC structure.
result GAS converges faster and more reliably than existing methods.
Misspecified Recoveryq-fin.MF
Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk-adjusted discounting, we use Perron-Frobenius Theory to isolate a positive martingal…
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…
Paper proposes a machine learning method to predict sale efficacy.
problem Determining the efficacy of online sales from discounts alone.
method Machine learning-based heuristic using Support Vector Machine.
result Predicts sale efficacy with 91.11% accuracy.