
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES


Time 
Talk Title and Abstract 
Tuesday, Aug 6
2:00pm

Matheus Grasselli (slides)
Energy, Finance, and Macroeconomics
Like many other areas in financial mathematics, the study
of commodities, energy, and environmental finance developed
as a branch of financial economics, and is therefore based
on equilibrium, rational expectations, representative
agents, and other notions from mainstream economics. Since
the 200708 financial crisis, however, these shaky foundations
for the subject have been vigorously attacked, and several
alternative views gained prominence.
In this talk I'll informally review some strands of heterodox
macroeconomics, with emphasis on the work of Hyman Minsky
and Wynne Godley. In particular, I'll describe the framework
of stockflow consistent models and give an explicit example
related to Green Jobs based on a recent proposal by Antoine
Godin (2012).

Wednesday, Aug 7
2:00pm

Matt Davison, University of Western Ontario (slides)
Management of Wind Energy with Storage: Structural Implications
for Policy and Market Design
The generation resource uncertainty induced by significant
wind capacity raises concerns about grid security, price stability
and revenue adequacy. One of the most promising solutions is the use
of utility scale energy storage, though the question of general implementation
of this strategy remains unanswered. In this talk, I present a simplified
model to show that there exist simple rules governing optimal bidding
and energy storage rules from a hybrid windstorage system. The heuristics
developed consider the combination of storage efficiency, electricity
price and shortfall penalty and wind forecast characteristics to guide
the decision of whether to bid energy into the electricity market.
We develop the optimal strategy for use of a simplified system
of an energy storage unit with a wind generator. The solution is
analyzed as a dynamic program, in a simplified framework over a
multiperiod planning horizon. The analysis of the solution under
all regimes yields insightful structural solutions regarding the
conditions under which the wind generator should bid into the energy
market and when they should not.
For the simple case in which each period is, independent of previous
periods, equally likely to be sufficiently windy to generate power,
we rigorously prove that for all combinations of wind probability,
shortfall penalty, and round trip efficiency, it is always optimal
to bid energy into the market when storage is full, and always optimal
to avoid a shortfall penalty by using stored energy, regardless
of the magnitude of the penalty and regardless of the time remaining
in the planning horizon. However, when stored energy is unavailable,
the optimal bid rule depends on the penalty size as a function of
storage loss characteristics, wind probability, and time remaining
in the planning horizon. While analytic results are not available
in the more complicated case of a time varying probability of wind,
numerical results show results which, while broadly consistent with
the constant wind probability case, vary from that case in interesting
ways.
The results of this paper provide insight into the implications
of forecast accuracy and market design on the need for storage.
This analysis allows additional conclusions to be drawn about the
value of various storage technologies based on their capacity and
efficiency characteristics. However, the most important contribution
of this work is the understanding of the importance of market penalties
in encouraging participants to either improve forecasting ability
or, perhaps more realistically, contract storage to mitigate shortfall
risk. This is joint work with Lindsay Anderson (Cornell) and Natasha
Burke (Western).

Monday, Aug 12
3:30pm

Rene Aid, EDF R&D and Finance for Energy Market Research
Centre
A probabilistic numerical method for optimal multiple switching
problem applied to investments in electricity generation
Free boundary problems naturally arise when dealing with
investment decisions in electricity generation. The problem is so
complex in terms of operating constraints, alternatives and random
factors that simplifications have to be made. The common approach
in the electric industry is still to rely on generation expansion
planning methods. Those models use a detailed representation of the
electric system to provide a single policy that will satisfy the future
demand. Thanks to the development of real options methodology, alternative
models have been developed in the economic and mathematical literature.
Those simplified models provide insights of the optimal investment
strategy in electricity generation.
In this talk, we will first provide a review of the most salient
examples of those models. In particular, we will see that, although
they provide an understanding of the investment dynamic, they are
limited to small dimension. So, we will show how the progress made
in the last decade by numerical methods for optimal switching problem
can be used to overcome the dimensionality issue. We will give the
example of a high dimensional electricity generation investment
model. This model takes into account electricity demand, cointegrated
fuel prices, carbon price and random outages of power plants. It
computes the optimal level of investment in each generation technology,
considered as a whole, w.r.t. the electricity spot price. This electricity
price is itself constructed according to an extended structural
model. In particular, it is a function of the random processes as
well as the installed capacities. The evolution of the optimal generation
mix is illustrated on a realistic numerical problem in dimension
8, i.e. with 2 different technologies and 6 random processes. This
talk is based on a joint work with Luciano Campi, Nicolas Langrene
and Huyen Pham.

Tuesday, Aug 13
3:30pm 
Ivar Ekeland, UBC and Paris Dauphine (slides)
No turning back: growth theory and sustainable developmen
We present a model for sustainable development, which is
an extension of the classical Ramsey model for economic growth. The
extension consists in adding to the criterion of the representative
agent a term, due to Chichilnisky, which represents concern for the
distant future. We show that, in addition to the business as usual
strategy, corresponding to the optimal solution in the Ramsey model,
with no concern for the future, there are additional strategies, but
that they cannot build up natural capital once it has been destroyed.

Monday, Aug 19
2:00pm 
Lane P. Hughston, University College London (slides)
Social Discounting and the Long Rate of Interest
The wellknown theorem of Dybvig, Ingersoll and Ross shows
that the long zerocoupon rate can never fall. This result, which
although undoubtedly correct has been regarded by many as counterintuitive
and even pathological, stems from the implicit assumption that the
longterm discount function has an exponential tail. We revisit the
problem in the setting of modern interest rate theory, and show that
if the long simple interest rate (or Libor rate) is finite, then this
rate (unlike the zerocoupon rate) acts viably as a state variable,
the value of which can fluctuate randomly in line with other economic
indicators. New interest rate models are constructed, under this hypothesis,
that illustrate explicitly the good asymptotic behaviour of the resulting
discount bond system. The conditions necessary for the existence of
such hyperbolic long rates turn out to be those of socalled social
discounting, which allow for longterm cash flows to be treated as
broadly as those of the short or medium term. As a consequence, we
are able to provide a consistent arbitragefree valuation framework
for the costbenefit analysis and risk management of longterm social
projects, such as those associated with sustainable energy, resource
conservation, space exploration, and climate change. (Joint work with
Dorje C. Brody, Brunel University. Paper available at arXiv:1306.5145)

Wednesday, Aug 21
2 p.m. 
John Chadam, University
of Pittsburgh
The inverse boundary crossing problem for diffusions
A summary of our work on the inverse boundary crossing problem
for diffusions will be presented. To begin, the direct and inverse
problems will be described in their probabilistic, PDE and integral
equation settings. Our previous results on the existence and uniqueness
of the solution to the inverse problem in the PDE setting will be
outlined. More recently a verification theorem was established showing
that this solution solves the probabilistic version of the problem.
Results on the initial behavior and continuity of the boundary will
be described. Finally, a numerical scheme based on the equivalent
integral equation formulation of the problem will be discussed.
(Joint work with Xinfu Chen, Lan Cheng & David Saunders)

Thursday, Aug 22
2 p.m.

Tim Leung, Columbia University
Leveraged ETFs and their Options
We discuss the performance of leveraged exchangedtraded funds
(LETFs) and the implied volatilities of LETF options, with an emphasis
on the role of different leverage ratios. First, we examine the
empirical returns and implied volatility surfaces for LETFs based
on the S&P 500 index, and introduce the concept of "moneyness
scaling" to enhance their comparison with nonleveraged ETF
implied volatilities. Under a multiscale stochastic volatility framework,
we apply asymptotic techniques to derive an approximation for both
the LETF option price and implied volatility. The approximation
formula reflects the role of the leverage ratio, and thus allows
us to link implied volatilities of options on an ETF and its leveraged
counterparts. Our result is applied to quantify matches and mismatches
in the level and slope of the implied volatility skews for various
LETF options using data from the underlying ETF option prices. This
reveals some apparent biases in the leverage reflected in the different
products, long and short with leverage ratios two times and three
times.

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