Minimum consumption and transitional dynamics in wealth distribution

This paper investigates quantitatively how initial wealth holding differences across households are propagated through time in a one sector growth model economy. A key feature of the model is that household consumption cannot fall below a positive level each period. The existence of a minimum consumption requirement implies that the Intertemporal Elasticity of Substitution not only differs across households but also changes differently over time. This model is calibrated to match some key aggregate statistics of the U.S. economy. We find that, as in the data, the wealth distribution in our benchmark model economy exhibits a (brief) period of increasing inequality, a short period in which inequality diminishes and a steady level of inequality along the balanced growth path. However, our model illustrates that the evolution of inequality is very sensitive to the length of the transition path. Additionally, our model predicts an upsurge in wealth inequality following the productivity slowdown in the 1970s.     

Automatic balancing mechanisms for notional defined contribution accounts in the presence of uncertainty

The notional defined contribution model combines pay-as-you-go financing and a defined contribution pension formula. This paper aims to demonstrate the extent to which liquidity and solvency indicators are affected by fluctuations in economic and demographic conditions and to explore the introduction of an automatic balancing mechanism (ABM) into the pension scheme. We demonstrate that the introduction of an ABM reduces the volatility of the buffer fund and that, in most cases, the automatic mechanism that re-establishes solvency produces the highest value of the risk-adjusted notional factor.     

Bank Competition with Financing and Savings Substitutes

This paper models the banking competition in loan and deposit markets on two levels. We measure the competition among different banks and among banks and non-bank financing and saving alternatives. We estimate a model of demand, cost, and market equilibrium equations for differentiated products by using data from the confidential reports that Spanish banks provide to the Bank of Spain during the period from 1988 to 2003. This database contains information on the effective interest rates on new loans and deposits, and the expected loan losses obtained from the Spanish Credit Register. The estimated price elasticities show that the products offered by different banks are close substitutes, which puts pressure on the banks’ profits margins. However, the substitutability between bank and non-bank products is much lower than the substitutability among products offered by different banks. The results also show that Spain’s entrance into the Eurozone did not cause a structural change in the demand and cost conditions of Spanish banks. The banks financed most of the imbalances between bank loans and domestic deposits before the crisis through the interbank market.     

Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.     

An expansion in the model space in the context of utility maximization

In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian), an explicit second-order expansion formula for the power investor’s value function—seen as a function of the underlying market price of risk process—is provided. This allows us to provide first-order approximations of the optimal primal and dual controls. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.     

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the linear part of the drift being a generator of a \(C_{0}\)-semigroup) driven by an infinite-dimensional cylindrical Wiener process. In particular, we prove, under some sufficient conditions on the coefficients, the existence and uniqueness of solutions for these stochastic evolution equations in a class of Banach spaces satisfying the so-called \(H\)-condition. Moreover, we analyse the Markov property of the solutions.Secondly, we apply the abstract results obtained in the first part to prove the existence and uniqueness of solutions to the Heath–Jarrow–Morton–Musiela (HJMM) equations in weighted Lebesgue and Sobolev spaces.Finally, we study the ergodic properties of the solutions to the HJMM equations. In particular, we find a sufficient condition for the existence and uniqueness of invariant measures for the Markov semigroup associated to the HJMM equations (when the coefficients are time-independent) in the weighted Lebesgue spaces.Our paper is a modest contribution to the theory of financial models in which the short rate can be undefined.     

Energy and CO2 emission relationships in the NAFTA trading bloc: a multi-regional multi-factor energy input–output approach

The North-America Free Trade Agreement (NAFTA) has brought together the economies of Canada, Mexico, and the US into forming one of the largest trading blocs worldwide (within the top CO₂ emitters). However, the current global protectionist discourse threatens the agreement. This paper analyzes the energy and energy-related CO₂ emission relationships between NAFTA countries in 2014 to gain insights into the climate change implications of current integration and the possible cancelation of the agreement. The analysis is performed with a multi-regional version of the multi-factor energy input–output model. The results show that NAFTA has not built a single integrated energy system, though it has helped reduce energy-related CO₂ emissions. Moreover, if NAFTA is not revoked, further integration would depend on the capacity of the Mexican energy sector to converge to the performance of its trade partners’ energy sectors. Conversely, a broken deal would induce negative environmental externalities.