7,173 research outputs found
Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs
In this paper we study a continuous time stochastic inventory model for a
commodity traded in the spot market and whose supply purchase is affected by
price and demand uncertainty. A firm aims at meeting a random demand of the
commodity at a random time by maximizing total expected profits. We model the
firm's optimal procurement problem as a singular stochastic control problem in
which controls are nondecreasing processes and represent the cumulative
investment made by the firm in the spot market (a so-called stochastic
"monotone follower problem"). We assume a general exponential L\'evy process
for the commodity's spot price, rather than the commonly used geometric
Brownian motion, and general convex holding costs.
We obtain necessary and sufficient first order conditions for optimality and
we provide the optimal procurement policy in terms of a "base inventory"
process; that is, a minimal time-dependent desirable inventory level that the
firm's manager must reach at any time. In particular, in the case of linear
holding costs and exponentially distributed demand, we are also able to obtain
the explicit analytic form of the optimal policy and a probabilistic
representation of the optimal revenue. The paper is completed by some computer
drawings of the optimal inventory when spot prices are given by a geometric
Brownian motion and by an exponential jump-diffusion process. In the first case
we also make a numerical comparison between the value function and the revenue
associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and
section
An optimal trading problem in intraday electricity markets
We consider the problem of optimal trading for a power producer in the
context of intraday electricity markets. The aim is to minimize the imbalance
cost induced by the random residual demand in electricity, i.e. the consumption
from the clients minus the production from renewable energy. For a simple
linear price impact model and a quadratic criterion, we explicitly obtain
approximate optimal strategies in the intraday market and thermal power
generation, and exhibit some remarkable properties of the trading rate.
Furthermore, we study the case when there are jumps on the demand forecast and
on the intraday price, typically due to error in the prediction of wind power
generation. Finally, we solve the problem when taking into account delay
constraints in thermal power production.Comment: 39 pages, 11 figure
Pricing average price advertising options when underlying spot market prices are discontinuous
Advertising options have been recently studied as a special type of
guaranteed contracts in online advertising, which are an alternative sales
mechanism to real-time auctions. An advertising option is a contract which
gives its buyer a right but not obligation to enter into transactions to
purchase page views or link clicks at one or multiple pre-specified prices in a
specific future period. Different from typical guaranteed contracts, the option
buyer pays a lower upfront fee but can have greater flexibility and more
control of advertising. Many studies on advertising options so far have been
restricted to the situations where the option payoff is determined by the
underlying spot market price at a specific time point and the price evolution
over time is assumed to be continuous. The former leads to a biased calculation
of option payoff and the latter is invalid empirically for many online
advertising slots. This paper addresses these two limitations by proposing a
new advertising option pricing framework. First, the option payoff is
calculated based on an average price over a specific future period. Therefore,
the option becomes path-dependent. The average price is measured by the power
mean, which contains several existing option payoff functions as its special
cases. Second, jump-diffusion stochastic models are used to describe the
movement of the underlying spot market price, which incorporate several
important statistical properties including jumps and spikes, non-normality, and
absence of autocorrelations. A general option pricing algorithm is obtained
based on Monte Carlo simulation. In addition, an explicit pricing formula is
derived for the case when the option payoff is based on the geometric mean.
This pricing formula is also a generalized version of several other option
pricing models discussed in related studies.Comment: IEEE Transactions on Knowledge and Data Engineering, 201
Forecasting OPEC oil price: a comparison of parametric stochastic models
Most academic papers on oil price forecasting have frequently focused on the use of WTI and European Brent oil price series with little focus on other equally important international oil price benchmarks such as the OPEC Reference Basket (ORB). The ORB is a weighted average of 11-member countries crude streams weighted according to production and exports to the main markets. This paper compares the forecasting accuracy of four stochastic processes and four univariate random walk models using daily data of OPEC Reference Basket series. The study finds that the random walk univariate model outperforms the other stochastic processes. An element of uncertainty was introduced into the point estimates by deriving probability distribution that describes the possible price paths on a given day and their likelihood of occurrence. This will help decision makers, traders and analysts to have a better understanding of the possible daily prices that could occur. JEL Classification Numbers: E64; C22; Q30 Keywords: Oil Price Forecasting, Probability Distributions, and Forecast Evaluation Statistics, Brownian Motion with Mean Reversion process, GARCH Model
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