A general endogenous grid method for multi-dimensional models with non-convexities and constraints

The endogenous grid method (EGM) significantly speeds up the solution of stochastic dynamic programming problems by simplifying or completely eliminating root-finding. We propose a general and parsimonious EGM extended to handle (1) multiple continuous states and choices, (2) multiple occasionally binding constraints, and (3) non-convexities such as discrete choices. Our method enjoys the speed gains of the original one-dimensional EGM, while avoiding expensive interpolation on multi-dimensional irregular endogenous grids. We explicitly define a broad class of models for which our solution method is applicable, and illustrate its speed and accuracy using a consumption–saving model with both liquid assets and illiquid pension assets and a discrete retirement choice.     

Monitoring as a partially observable decision problem

Monitoring is an important and costly activity in resource management problems such as containing invasive species, protecting endangered species, preventing soil erosion, and regulating contracts for environmental services. Recent studies have viewed optimal monitoring as a Partially Observable Markov Decision Process (POMDP), which provides a framework for sequential decision making under stochastic resource dynamics and uncertainty about the resource state. We present an overview of the POMDP framework and its applications to resource monitoring. We discuss the concept of the information content provided by monitoring systems and illustrate how information content affects optimal monitoring strategies. Finally, we demonstrate how the timing of monitoring in relation to resource treatment and transition can have substantial effects on optimal monitoring strategies.     

Momentum in the Chinese Stock Market: Evidence from Stochastic Oscillator Indicators

ABSTRACT

We explore whether investors earn profits through the use of stochastic oscillator indicators (SOI) for trading stocks. The results reveal that investors might use momentum strategies when trading constituent stocks of SSE 50 as the overbought trading signals emitted by SOI. We infer that the results might be caused by herding behaviors of Chinese investors since overoptimistic moods are likely to exist as evidenced by the 80 percent trading volume traded by individual investors in the Chinese stock market.     

PRICE SETTING OF MARKET MAKERS: A FILTERING PROBLEM WITH ENDOGENOUS FILTRATION

This paper studies the price‐setting problem of market makers under risk neutrality and perfect competition in continuous time. The classic approach of Glosten–Milgrom is followed. Bid and ask prices are defined as conditional expectations of a true value of the asset given the market makers' partial information that includes the customers' trading decisions. The true value is modeled as a Markov process that can be observed by the customers with some noise at Poisson times. A mathematically rigorous analysis of the price‐setting problem is carried out, solving a filtering problem with endogenous filtration that depends on the bid and ask price processes quoted by the market maker. The existence and uniqueness of the bid and ask price processes is shown under some conditions.     

Sustainable hub location under mixed uncertainty

This paper addresses a novel sustainable hub location problem (SHLP) in which two new environmental-based cost functions accounting for air and noise pollution of vehicles are incorporated. To cope with uncertain data incorporated in the model, a mixed possibilistic–stochastic programming approach is proposed to construct the crisp counterpart. A simulated annealing (SA) and an imperialist competitive algorithm (ICA) with a new solution representation are developed to solve real-sized instances whose performances are compared with a proposed lower bound. Finally, some computational experiments are provided to demonstrate the effectiveness of the proposed model and solution approaches.     

Maximizing benefits in project selection: a hybrid approach

Charitable foundations and government programmes should endeavour to allocate their limited resources to best serve their constituents. Yet, mathematical programming techniques are rarely used despite overwhelming evidence of their superiority in selecting projects that yield higher levels of total benefits. We present a novel ‘hybrid selection model’ that combines binary linear programming and heuristic rank-based models applied to two case studies. The first case focuses on providing services to women and shows a hybrid model would have selected the top three ‘signature’ projects and maintained an above-average overall project benefit while securing a 180% improvement in the number of projects funded, a 66% improvement in the number of women served and a 132% improvement in the total benefit achieved. In the second case, we apply the hybrid approach to data from the US government’s largest forest preservation programme and demonstrate that the hybrid approach could allow the programme to select up to 11 top-scoring projects while still achieving a 97% gain in the total overall benefit compared to their traditional method. These case studies show that the hybrid approach has the potential to be applied in a variety of settings and improve how foundations and programmes achieve their goals.     

The generalized lock scheduling problem: An exact approach

The present paper introduces an integrated approach to solving the generalized lock scheduling problem. Three interrelated sub problems can be discerned: ship placement, chamber assignment and lockage operation scheduling. In their turn, these are closely related to the 2D bin packing problem, the assignment problem and the (parallel) machine scheduling problem respectively. In previous research, the three sub problems mentioned were considered separately, often using (heuristic) interaction between them to obtain better solutions. A mixed integer linear programming model is presented and applied to instances from both inland locks and locks in a tide independent port. The experiments show that small instances incorporating a wide range of real-life constraints can be solved to optimality.     

Short-time at-the-money skew and rough fractional volatility

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.     

Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model

The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. This paper investigates whether the use of models which allow for negative interest rates can improve option pricing and implied volatility forecasting. This is done with special attention to foreign exchange and index options. To this end, we carried out an empirical analysis on the prices of call and put options on the US S&P 500 index and Eurodollar futures using a generalization of the Heston model in the stochastic interest rate framework. Specifically, the dynamics of the option’s underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. Explicit formulas for the transition probability density function and moments are derived. These formulas are used to estimate the model parameters efficiently. Three empirical analyses are illustrated. The first two show that the use of models which allow for negative interest rates can efficiently reproduce implied volatility and forecast option prices (i.e. S&P index and foreign exchange options). The last studies how the US three-month government bond yield affects the US S&P 500 index.     

How should Engel's law be formulated?

Engel's law expresses a “negative stochastic association” of income and the proportion of income that is spent on food. However, there are many quite different notions of “negative stochastic association” and consequently there are different ways of defining Engel's law. We relate these different concepts to Engel's original statistical analysis and show that one must give credit to Engel for the first non-parametric statistical analysis of budget-data.