Smooth solutions found for complex financial control problems.
problem Discounted reward control with unbounded discount rate.
method General assumptions and verification reasoning for HJB equation.
result Smooth classical solutions to HJB equation exist.
Repo rates are explained as a convexity effect from bond and derivative discount rates.
problem Explaining the observed basis between repo rates and bond prices.
method Using a Hull-White model, derived expressions for repo rates and extrapolation.
result Interpolated and extrapolated repo curves for bond-collateralised derivatives.
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.
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.
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…
Revises derivative pricing post financial crisis by defining a discount rate.
problem Derivative pricing became complex with XVA adjustments.
method Developed a binomial tree model for pricing with counterparty and funding risks.
result Coherent XVAs naturally result from decomposing the discount rate.
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.
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.
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 …
Proposes a new method for determining LGD discount rates based on cost of capital.
problem Determining an appropriate discount rate for LGD estimation.
method Market-consistent pricing of defaulted loan portfolios to infer discount rates.
result Discount rates reflect both undiversifiable risk and time value of money.
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.
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 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.
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 …
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.
Paper tackles time inconsistency in portfolio management with stochastic volatility and power utility.
problem Time inconsistency in portfolio management with stochastic volatility and power utility.
method Extended Hamilton Jacobi Bellman (HJB) equation, fixed point iteration, and linear parabolic PDE.
result Subgame perfect strategies are characterized and solved through numerical experiments.
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.
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…
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.
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…
This paper calculates the stock price covariance with correlated growth rates.
problem Determining the covariance of stock prices with correlated growth rates.
method Developed a formula for the covariance of random stock prices with correlated growth rates of dividends.
result A formula for the covariance of stock prices with correlated growth rates of dividends.
The paper develops a new discount rate for derivatives using imperfect securities as collateral.
problem Inconsistent and non-observable collateral rates in derivatives markets.
method Synthesizes effects of imperfect collateral into a new discount rate, employs break-even repo formulae, and uses linear programming for optimization.
result Liquidity value adjustment (LVA) can be significant for long-term derivatives portfolios.
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…
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…
Model shows consumption growth slows due to finite planet resources.
problem Understanding and predicting consumption growth in a finite planet context.
method Logistic model of consumption growth, cumulant expansion method.
result Social discount rates decline over time due to planetary resource constraints.
Paper offers a new method for valuing stocks with multiple growth rates.
problem Valuing stocks with complex growth patterns.
method Developed a general solution for the Dividend Discount Model.
result Improved precision in stock valuation.
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 well-known theorem of Dybvig, Ingersoll and Ross shows that the long zero-coupon rate can never fall. This result, which, although undoubtedly correct, has been regarded by many as surprising, stems from the implicit assumption that the long-term discount function has an exponential tail. We revisit the problem in …
Study shows ambiguity affects optimal timing in a two-dimensional model.
problem Understanding how ambiguity influences optimal timing in a two-dimensional setting.
method Analyzes a two-dimensional optimal stopping problem with ambiguity in a multifactor model.
result Ambiguity affects the rate at which the problem is discounted, not just the growth rate of underlying processes.
A firm with heterogeneous shareholders optimizes dividends under ambiguity aggregation.
problem Optimizing dividends for a firm with heterogeneous shareholders under ambiguity aggregation.
method Characterizing equilibrium dividends using a partition of the state space.
result Time-homogeneous equilibrium dividend law characterized by a partition of the state space.
Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.
problem Convergence rate of empirical minimizer for unbounded functions with fast growth.
method Analyzes L1-distance convergence rate of the empiric minimizer for coercive functions sampled with noise. result Convergence rate is bounded above by ann−1/q, where q is the dimension and an=o(nε) for every ε>0. Enhances xVA valuation with initial margin and CSA discounting.
problem Inconsistency in discount curves and aggregation of trades.
method Unified approach using BSDEs with initial margin, CSA discounting, and non-linear aggregation.
result Consistent xVA valuation with trade-specific discount curves.
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…
Study finds minimum growth rate for surface solutions.
problem Finding minimum growth rate for surface solutions.
method Analyzes minimal surface equation with zero boundary values over unbounded domains.
result Establishes lower bound for maximum solution values.
Investment project break-even point analyzed as discount rate changes.
problem Determining the break-even point for a simple investment project.
method Closed expression derived for break-even point Qf as a function of parameters.
result Qf is strictly increasing and convex in r, with strong influence of p and Cv.
This paper solves Siegel's paradox about future exchange rates.
problem Understanding future exchange rates and resolving Siegel's paradox.
method An unorthodox approach leading to an arbitrage-free solution.
result A formula describing all no-arbitrage forward exchange rates.
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.
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.
Study introduces new methods to estimate stock return rates.
problem Estimating the required rate of return for stocks and private companies.
method Maximum likelihood, Bayesian, and Kalman filtering methods applied to historical data.
result Suggested methods can accurately estimate the required rate of return.
The paper explores perpetual contracts in a financial market without arbitrage.
problem Modeling perpetual contracts in a continuous-time financial market.
method Derive model-free and semi-robust expressions for perpetual contracts' funding and discount rates.
result Explicit replication strategies for perpetual contracts are derived, relating them to traditional financial instruments.
The paper optimizes insurance strategies for two collaborating business lines.
problem Maximizing dividends and managing risk for two collaborating business lines.
method Closed-form solutions for optimal strategies, including dividend payout, reinsurance, and capital injection.
result Optimal strategies involve pure excess-of-loss reinsurance and transferring reserves to prevent ruin.
Paper provides uniform deviation bounds for unbounded loss functions, improving k-Means clustering bounds.
problem Uniform deviation bounds for unbounded loss functions, specifically k-Means clustering.
method Novel framework to obtain uniform deviation bounds for unbounded loss functions.
result Improved bounds for k-Means clustering under weak assumptions, achieving $\mathcal{O}\left(m^{-\frac12}
ight)$ rate.
New neural network rates for unbounded domains with weighted Sobolev spaces.
problem Improving neural network approximation rates for unbounded domains.
method Embedding results for weighted Fourier-Lebesgue spaces in weighted Sobolev spaces, followed by asymptotic approximation rates.
result Asymptotic approximation rates for shallow neural networks without curse of dimensionality for unbounded domains and Muckenhoupt weights.
The paper introduces a method to accurately price swaps and their Value at Risk (VaR) using dynamic trading and regression/simulation.
problem Theoretical and practical concerns about uncollateralized swaps and their risk not being fully hedged.
method Dynamic trading of CCP swaps, applying discount rates based on counterparty's or own bond curves, and using Longstaff-Schwartz regression and finite difference schemes.
result The uncollateralized swap can be fully replicated, and FVA is redefined as a liquidity or funding basis component of total valuation adjustment.
Defines risk-free portfolios and risk-free rate using gauge symmetries.
problem Identifying a consistent definition of risk-free rate in economics.
method Introduces three gauge invariant differential operators to define risk-free portfolios and identifies the risk-free rate as the return of an infinitely diversified portfolio.
result Identifies the risk-free rate as the return of an infinitely diversified portfolio and connects it to global price rescaling as a gauge symmetry.
Faster algorithms for solving multichain MDPs under average-reward criterion.
problem Navigating towards the best connected component in multichain MDPs.
method Developed algorithms to better solve the navigational subproblem, achieving faster convergence rates.
result Improved rates of convergence and sharper complexity measures for multichain MDPs.
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.
The paper analyzes optimal dividend and capital injection strategies under time-inconsistent preferences.
problem Optimal dividend and capital injection strategies under time-inconsistent preferences.
method Diffusion risk model with general discount functions, weak equilibrium definition, HJB equation system.
result Explicit solutions and threshold types of optimal strategies derived under different discount functions.