Existing emissions trading system (ETS) designs inhibit emissions but do not constrain warming to any fxed level, preventing certainty of the global path of warming. Instead, they have the indirect objective of reducing emissions. They provide poor future price information. And they have high transaction costs for implementation, requiring treaties and laws. To address these shortcomings, this paper proposes a novel double-sided auction mechanism of emissions permits and sequestration contracts tied to temperature. This mechanism constrains warming for many (e.g., 150) years into the future and every auction would provide price information for this time range. In addition, this paper proposes a set of market rules and a bottom-up implementation path. A coalition of businesses begin implementation with jurisdictions joining as they are ready. The combination of the selected market rules and the proposed implementation path appear to incentivize participation. This design appears to be closer to "first best" with a lower cost of mitigation than any in the literature, while increasing the certainty of avoiding catastrophic warming. This design should also have a faster pathway to implementation. A numerical simulation shows surprising results, e.g., that static prices are wrong, prices should evolve over time in a way that contradicts other recent proposals, and "global warming potential" as used in existing ETSs are generally erroneous.

This review presents the set of electricity price models proposed in the literature since the opening of power markets. We focus on price models applied to financial pricing and risk management. We classify these models according to their ability to represent the random behavior of prices and some of their characteristics. In particular, this classification helps users to choose among the most suitable models for their risk management problems.

We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from a calibrated pure local volatility model, a two-factor Heston-type LSV model (both with deterministic rates), and the stochastic (CIR) short rates. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion. The calibration procedure is performed on real-world market data for the EUR-USD currency pair and has a comparable run-time to the PDE calibration of a two-factor LSV model alone.

In this paper,we study the individual's optimal retirement time and optimal consumption under habitual persistence. Because the individual feels equally satisfied with a lower habitual level and is more reluctant to change the habitual level after retirement, we assume that both the level and the sensitivity of the habitual consumption decline at the time of retirement. We establish the concise form of the habitual evolutions, and obtain the optimal retirement time and consumption policy based on martingale and duality methods. The optimal consumption experiences a sharp decline at retirement, but the excess consumption raises because of the reduced sensitivity of the habitual level. This result contributes to explain the "retirement consumption puzzle". Particularly, the optimal retirement and consumption policies are balanced between the wealth effect and the habitual effect. Larger wealth increases consumption, and larger growth inertia (sensitivity) of the habitual level decreases consumption and brings forward the retirement time.

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. We envision that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates the non-decreasing benchmark floor process at each intermediate time. The control problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with reflection, we next transform the problem further into an equivalent auxiliary problem, which leads to a nonlinear Hamilton-Jacobi-Bellman (HJB) equation with a Neumann boundary condition. By employing the dual transform, the probabilistic representation and some stochastic flow analysis, the existence of the unique classical solution to the dual HJB equation is established. The verification theorem is carefully proved, which gives the complete characterization of the primal value function and the feedback optimal portfolio. The application to market index tracking is also discussed when the index process is modeled by a geometric Brownian motion.

This paper investigates the finite time risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. The Markov regime-switching process is assumed to be unobservable, which has countable states that affect default intensities of surviving assets. The stochastic control problem is formulated under partial observations of asset prices and default events. By proving a martingale representation theorem based on incomplete and phasing out filtration, we characterize the value function in an equivalent form. This allows us to connect the control problem to a quadratic BSDE with jumps, in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and establishing a uniform a priori estimates, we obtain the existence of a solution to the BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE.

General equilibrium macroeconomic models are a core tool used by policymakers to understand a nation's economy. They represent the economy as a collection of forward-looking actors whose behaviours combine, possibly with stochastic effects, to determine global variables (such as prices) in a dynamic equilibrium. However, standard semi-analytical techniques for solving these models make it difficult to include the important effects of heterogeneous economic actors. The COVID-19 pandemic has further highlighted the importance of heterogeneity, for example in age and sector of employment, in macroeconomic outcomes and the need for models that can more easily incorporate it. We use techniques from reinforcement learning to solve such models incorporating heterogeneous agents in a way that is simple, extensible, and computationally efficient. We demonstrate the method's accuracy and stability on a toy problem for which there is a known analytical solution, its versatility by solving a general equilibrium problem that includes global stochasticity, and its flexibility by solving a combined macroeconomic and epidemiological model to explore the economic and health implications of a pandemic. The latter successfully captures plausible economic behaviours induced by differential health risks by age.

In this article, we consider a compound Poisson-type model for households' capital. Using risk theory techniques, we determine the probability of a household falling under the poverty line. Microinsurance is then introduced to analyse its impact as an insurance solution for the lower income class. Our results validate those previously obtained with this type of model, showing that microinsurance alone is not sufficient to reduce the probability of falling into the area of poverty for specific groups of people, since premium payments constrain households' capital growth. This indicates the need for additional aid particularly from the government. As such, we propose several premium subsidy strategies and discuss the role of government in subsidising microinsurance to help reduce poverty.