Michel Denault

• Ph.D.
• Professor (Full) at HEC Montréal

We compute the Value of Saved Power: the value of replacing a unit of power with efficiency measures, delivering the same energy service. The way one would replace the cost of thousands of kilowatthours for heating, by the cost of insulating a house. Our analysis is especially relevant in a transition era, where power prices are poised to increase...

The decarbonization of power systems, while widely studied, seldom compares the cost implications of the underlying planning assumptions. For example , the time horizon that is considered, and the scope of regional cooperation , can have a significant impact on costs. To highlight the benefits of long-term, multi-stage, cooperative plans, we contra...

We solve a multi-stage stochastic expand-and-operate model to derive least-cost expansion plans reaching net-zero emissions from the power sector in 2050. Generation, storage and transmission decisions are included. Long-term uncertainties are modeled for both expansion costs of renewables and storage, and load growth. Parameters are tuned to a fiv...

The control of multi-reservoir hydropower systems is a crucial cogwheel in the current transition of power systems towards renewable energy. In particular in northern regions where inows vary enormously through the year, the satisfaction of storage constraints cannot be ensured at all times. We thus add chance constraints to the underlying Markov D...

The control of multi-reservoir hydropower systems is a crucial cogwheel in the current transition of power systems towards renewable energy. In particular in northern regions where inflows vary enormously through the year, the satisfaction of storage constraints cannot be ensured at all times. We thus add chance constraints to the underlying Markov...

This short note suggests two improvements for solving the goal-based wealth management problem proposed by Das, Ostrov, Radhakrishnan and Srivastav (2020). The first suggestion smoothes and improves the convergence of the approximate solutions towards the underlying, continuous solution either by using analytic solutions at the penultimate time poi...

This paper examines the dynamic, multiperiod portfolio choices of an investor facing predictable returns with volatility clustering and non-normalities, two pervasive stock return data characteristics. With a portfolio of one risk-free and one risky asset, we calibrate the model to the U.S. stock market and consider multiperiod choices, GARCH volat...

Simulation-and-regression algorithms have become a standard tool for solving dynamic programs in many areas, in particular financial engineering and computational economics. In virtually all cases, the regression is performed on the state variables, for example on current market prices. However, it is possible to regress on decision variables as we...

Simulation-and-regression methods have been recently proposed to solve multi-period, dynamic portfolio choice problems. In the constant relative risk aversion (CRRA) framework, the “value function recursion vs portfolio weight recursion” issue was previously examined in van Binsbergen and Brandt [24] and Garlappi and Skoulakis [14]. We revisit this...

In deregulated markets, electricity prices are typically characterized by four key features: seasonality, mean-reversion, the possibility of large downward or upward unexpected spikes, and volatility clustering. We propose a time-series price model with skewed and leptokurtic shocks, which displays all four features above. Importantly, the model fu...

We investigate the optimum control of a stochastic system, in the presence of both exogenous (control-independent) stochastic state variables and endogenous (control-dependent) state variables. Our solution approach relies on simulations and regressions with respect to the state variables, but also grafts the endogenous state variable into the simu...

The complementarity of two renewable energy sources, namely hydro and wind, is investigated. We consider the diversification effect of wind power to reduce the risk of water inflow shortages, an important energy security concern for hydropower-based economic zones (e.g. Québec and Norway). Our risk measure is based on the probability of a productio...

The estimation of physical intensity processes in the context of default risk is investigated here. Using data from Moody's Corporate Bond Default Database, a term structure of default probabilities for different rating classes is constructed each year from 1970 to 2001. Two specifications used for modeling the dynamics of the (risk-neutral) intens...

In designing protein libraries for selection, we must coordinate our capacity to create a large diversity of protein variants with the physical limitations of what we can actually screen. This chapter aims to bring the language of probabilities into the protein engineer's laboratory to answer some of our common questions: How can we most efficientl...

Lattice schemes for option pricing, such as tree or grid/partial differential equation (p.d.e.) methods, are usually designed as a discrete version of an underlying continuous model of stock prices. The parameters of such schemes are chosen so that the discrete version “best” matches the continuous one. Only in the limit does the lattice option pri...

We introduce a cutting-plane, analytic-center algorithm for strongly monotone variational inequalities (VIs). The approach extends that of Goffin et al. (1997) and Denault and Goffin (1999). The VI is still treated as a convex feasibility problem, with linear cuts progressively shrinking alocalization set that contains the solution of the VI. Howev...

We extend in two directions the Analytic Center, Cutting Plane Method for Variational Inequalities with quadratic cuts, ACCPM-VI(quadratic cuts), introduced by Denault and Goffin in 1998. First, we define a primal–dual method to find the analytic center at each iteration. Second, the Broyden–Fletcher–Goldfarb–Shanno Jacobian approximation, of quasi...

In the Black-Scholes framework, the American option pricing problem can be discretized into a finite-dimensional linear complementarity problem. We compare the numerical performances of three algorithms for the linear complementarity problem: the pivotal algorithms of Lemke and of Boriçi and Lüthi, and the iterative approach "Projected Successive O...

The allocation problem stems from the diversification e#ect observed in risk measurements of financial portfolios: the sum of the risk measures of many portfolios is typically larger than the risk of all portfolios taken together. The allocation problem is to apportion this "diversification advantage" to the portfolios in a fair manner, to obtain n...

We introduce an algorithm for strongly monotone variational inequalities (VIs). The approach extends that of [12] and [8], in that the VI is treated as a convex feasibility problem, with separating cuts being generated at the analytic center of a set known to contain the solution of the VI. Our approach uses quadratic, ellipsoidal cuts instead of l...

We present an algorithm for variational inequalities VI( F\mathcal{F} , Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping F\mathcal{F} is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one...

The first aim of this paper is to provide a comparison between the generic characteristics of the detection-by-appearance and the detection-by-behaviour models for malicious software intrusion detection, and thus to discuss the efficiency of intrusion detection systems based on AI technologies. We introduce the SECURENET system, an experimental int...