The Smith-Wilson method is analyzed for its peculiar hedges and negative discount factors.
problem Analyzing the Smith-Wilson method for discounting under EU regulation Solvency II.
method Novel stochastic representation of the Smith-Wilson method for hedging analysis.
result Negative discount factors and singularities in convergence criterion are linked.
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.
Study negative discount rate effects on perpetual options in Lévy models.
problem Negative discount rate impacts perpetual American and Swing options in Lévy models.
method Analyze perpetual American and put options in exponential Lévy models with negative discount rate, identify critical continuation prices, and generalize to Swing type problems.
result Double continuation region arises in negative discount rate cases, identified by critical prices.
This paper studies a class of optimal multiple stopping problems driven by Lévy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher rate than the original d…
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.
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 O ( log T / 1 − λ ) O(\sqrt{\log T/1-λ}) O ( log T /1 − λ ) discounted regret across a continuous interval of discount factors. Optimizes spending by adjusting a discount factor modelled as an exponential CIR process.
problem Maximizing discounted spendings/dividend payments given an exponential CIR discounting factor.
method Analytical and numerical methods for deterministic and stochastic surplus processes.
result Explicit expressions for optimal strategies in deterministic cases, and constant-barrier strategies for small volatility in stochastic cases.
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.
High subjective discount and risk aversion contradict financial data.
problem Inconsistent asset pricing with financial stylised facts.
method Analyzing capital market equilibrium restrictions.
result Subjective discount and risk aversion cannot be high simultaneously.
A new method maps value estimates to logarithmic space to enable lower discount factors in reinforcement learning.
problem The poor performance of low discount factors in reinforcement learning.
method Introducing a logarithmic mapping to value estimates.
result The method enables lower discount factors, solving challenging reinforcement learning problems.
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.
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 …
This work bridges hyperbolic discounting in RL with exponential discounting.
problem Hyperbolic discounting in reinforcement learning models.
method Implemented a hyperbolic discounting RL agent and demonstrated its effectiveness.
result Hyperbolic discounting can be approximated using familiar RL techniques.
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 …
Tests factor models by decomposing market into body and tail legs, revealing inconsistent results.
problem Inconsistency between factor models and market behavior.
method Decomposes market into body and tail legs, testing factor models at daily and monthly frequencies.
result q5 model shows inconsistent results, with negative body and positive tail alphas at all split ratios.
Study optimal stopping for American call options with random time-horizon in Lévy models.
problem Optimal stopping of American call options in random time-horizon under Lévy models.
method Model random time-horizon as Omega default clock, analyze value function under different q q q and y y y . result Different values of q q q and y y y lead to various optimal strategies (up-crossing, two-sided exit). 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…
This paper improves MARL for networked systems through new protocols and discount factors.
problem Improving control in networked systems using multi-agent reinforcement learning.
method Formulated as a spatiotemporal Markov decision process, introduced a spatial discount factor, and proposed NeurComm.
result Appropriate spatial discount factor enhances learning curves of non-communicative MARL algorithms.
Proves existence of long bond, long forward measure, and long-term factorization in HJM models.
problem Existence of long bond, long forward measure, and long-term factorization in HJM models.
method Function space framework of Filipovic (2001) and sufficient condition on the weight in the Hilbert space of forward rate volatility curves.
result Existence of long bond volatility process, long bond process, and long-term factorization of SDF.
Study decomposes market portfolio into body and tail legs, revealing systematic differences.
problem Understanding the relationship between body and tail components in market portfolios.
method Decomposes CRSP market portfolio into body and tail legs, analyzes their recombination identity.
result Recombination identity holds for all models but not for all, indicating systematic differences.
Study on CEF discount in Bangladesh, finds size and maturity impact, turnover negative.
problem Exploring the discount puzzle in closed-end mutual funds in Bangladesh.
method Fixed effects panel regression with diagnostic tests.
result Fund size and maturity positively impact CEF discount, turnover negatively impacts.
A study finds that only a few factors explain corporate bond risk, rendering extensive bond factor literature redundant.
problem The redundancy of extensive bond factor literature in explaining corporate bond risk premia.
method Bayesian Model Averaging Stochastic Discount Factor analysis of 18 quadrillion models.
result A Bayesian Model Averaging SDF explains risk premia better than low-dimensional models, with an out-of-sample Sharpe ratio of 1.5 to 1.8.
New Q-learning algorithm reduces sample complexity for large discount factors.
problem Large discount factors make Q-learning algorithms inefficient.
method Introduces a new Q-learning algorithm with uniformly bounded sample complexity.
result The new algorithm achieves asymptotic covariance that is a quadratic in 1 / ( 1 − ρ ∗ γ ) 1/(1- ρ^* γ) 1/ ( 1 − ρ ∗ γ ) . 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.
Market portfolio decomposed into body and tail legs
problem Separation of market portfolio into body and tail legs
method Dynamic value-weighted body and tail legs
result Recombination identity holds for all models
Q-Learning overestimation bias influenced by learning rate, discount factor, and reward signal.
problem Overestimation bias in Q-Learning algorithm.
method Investigated the influence of learning rate, discount factor, and reward signal on Q-Learning's overestimation bias. Tuned parameters and used an exponential moving average of reward signal.
result Q-Learning can achieve more accurate value estimates by tuning parameters and using an exponential moving average of reward signal.
Optimality of threshold strategies proven for Lévy models with discounting.
problem Proving optimality of threshold strategies in Lévy models with discounting.
method Average problem approach to prove optimality of threshold strategies for Lévy models with continuous additive functional discounting.
result Simpler and neater proofs for qualitative properties of optimal thresholds in recursive optimal stopping problems.
New concept of Blackwell regret for reinforcement learning with sparse rewards.
problem Sparse rewards in long horizon MDPs.
method Formalization of myopic discount factors, value functions, and policies in terms of Blackwell optimality; introduction of Blackwell regret.
result Selecting a discount factor for zero Blackwell regret becomes arbitrarily hard in long horizon MDPs.
The paper proposes a method to discount backtest PnLs due to in-sample overfitting.
problem In-sample overfitting in backtest-based investment strategies.
method A simple framework to model and quantify in-sample PnL overfitting.
result Computes the appropriate discount factor for PnLs of in-sample investment strategies.
The study analyzes historical interest rates to predict future discount rates and their implications on climate change.
problem Predicting future discount rates to inform climate change mitigation policies.
method Constructed real interest rates using historical data and a stochastic model (Ornstein-Uhlenbeck).
result Only 4 out of 14 countries have positive long-run discount rates, suggesting urgent action on climate change.
Empirical study on long-term discount rates using historical bond prices.
problem Estimating long-term real interest rates and discount rates from historical bond data.
method Using Fourier transforms to derive the discount function and fitting it to historical data.
result Estimated long-term discount rates of 1.7% for UK and 2.2% for US.
Study reveals a hidden cost in derivatives markets through option-implied discount factors.
problem The hidden cost in derivatives markets, not visible in price space.
method Minute-level NBBO data on options, reduced-form specification linking carry gap to implementation risk, trading frictions, and financial conditions.
result An annualized carry gap exists, linked to implementation risk and financial conditions.
The paper reviews historical and modern approaches to asset pricing probability measures.
problem Constructing or selecting probability measures for asset pricing.
method Historical review of various approaches including state price theory, martingale measures, and modern data-driven methods.
result Modern asset pricing involves constructing, transforming, or selecting probability measures to represent market prices.
Deep neural networks decompose SDF into linear and nonlinear components.
problem Constructing accurate stochastic discount factors (SDFs) for pricing.
method Additive decomposition of a deep neural network trained to construct SDFs.
result The PTK representation delivers significant performance gains in equity data.
Study uses put-call parity to estimate cost of funding in equity derivatives markets.
problem Estimating the cost of funding in active equity derivative markets.
method Develops a method using European put and call prices to recover the implicit discount factor and cost of funding.
result Identifies the cost of funding in major equity markets, showing it is typically around 34 basis points above OIS.
The paper proposes a new SDF scaled by time-varying volatility from S&P 500 options.
problem Estimating the SDF from option prices and predicting the equity premium.
method Utilizes S&P 500 options data to recover a stable, non-monotonic SDF.
result The SDF exhibits a hump on the put side, which transitions into a W-shape with maturity.
2024 saw Bitcoin ETF approval, offering regulated exposure.
problem Understanding unique liquidity risks in Bitcoin ETFs.
method Analyzed premium/discount patterns in first four months.
result Premium/discount behavior differs from traditional ETFs.
The paper factors long-term affine pricing kernels into two components.
problem Understanding long-term behavior of affine pricing kernels.
method Long-term factorization into discounting rate and martingale component.
result Explicit identification of long bond volatility and martingale component volatility.
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…
This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switch according to a finite…
Solves equity premium puzzle with time-varying variables.
problem Equity premium puzzle.
method Consumption Capital Asset Pricing Model with time-varying subjective time discount factors.
result Calculated coefficient of relative risk aversion (CRRA) is around 4.40.
Paper proposes an efficient RL algorithm for discounted MDPs using feature mapping.
problem Efficient reinforcement learning for large state and action spaces.
method Uses feature mapping to represent states and actions in a low-dimensional space, proposing a novel algorithm with polynomial regret bound.
result Achieves a O ( d T / ( 1 − γ ) 2 ) O(d\sqrt{T}/(1-γ)^2) O ( d T / ( 1 − γ ) 2 ) regret bound, near-optimal up to a ( 1 − γ ) − 0.5 (1-γ)^{-0.5} ( 1 − γ ) − 0.5 factor. Paper solves discounted stochastic games with near-optimal time and sample complexity.
problem Solving discounted stochastic two-player games with optimal complexity.
method Generalizes Q-learning to two-player strategy computation, overcoming limitations of existing methods.
result Near-optimal ε ε ε -strategy computation with polylogarithmic factors in 1 − γ 1 - γ 1 − γ and ε − 2 ε^{-2} ε − 2 . Policy gradient methods do not optimize the discounted objective, leading to suboptimal results.
problem Understanding the true optimization objective of policy gradient methods.
method Analyzing the update direction of policy gradient methods and proving it is not the gradient of any function.
result Policy gradient methods do not optimize the discounted objective, leading to suboptimal results.
Model shows how discount rates affect intergenerational equity in climate mitigation.
problem Intergenerational equity in climate mitigation decisions.
method Extended DICE model with stochastic discount rates and financing extensions.
result Discount-rate uncertainty amplifies intergenerational inequality in climate mitigation.
New Q Q Q -learning method reduces variance and achieves optimal sample complexity.
problem Improving Q Q Q -learning to reduce variance and improve sample efficiency. method Introduces variance-reduced Q Q Q -learning and analyzes its sample complexity. result Achieves minimax optimal sample complexity for estimating optimal Q Q Q -function. We find a condition for stable asset pricing models.
problem Existence and uniqueness of equilibrium asset prices.
method Exact necessary and sufficient condition derived through stochastic discount factor decompositions.
result Sharpens and improves previous results on asset pricing.
Optimal online linear regression in dynamic environments using discounted Vovk-Azoury-Warmuth forecaster.
problem Achieving optimal performance in dynamic online linear regression without prior knowledge.
method Developed a discounted variant of the Vovk-Azoury-Warmuth forecaster to achieve optimal dynamic regret guarantees.
result Achieved dynamic regret of the form $O\left(d\log(T)\vee \sqrt{dP_{T}^γ(\vec{u})T}
ight)$ , with a learnable discount factor.