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Central and local governments around the world are seeking investments from private firms to create smart city solutions. Motivated by this, we model an investor and a local government with a Stackelberg game. The investor has a CARA (or exponential) utility function and she has an option to acquire data dynamically and use that in a Bayesian predictive model to forecast the quality sensitivity of demand before her investment decision. The government chooses the highest price such that demand quantity is above a minimum threshold. We prove comparative statics under the dynamic information acquisition and the Stackelberg game. We show that borrowing-constrained or highly risk-averse investors have low demand for information. Fur- thermore, the falling marginal cost of information driven by smart cities’ datasets and analytics raises investment amounts and leverage, which leads to higher losses during crises. Finally, we show that leverage constraints are effective in mitigating losses during crises.

We consider optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the basket price and (ii) when he receives only noisy observations on the basket price. We derive the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds in both cases. The compositions of the funds in the two cases are the same, but in general the investor's allocations of his wealth into these funds will differ. However, in the particular case when the investor has constant relative risk-aversion (CRRA) utility, his optimal investment allocations into these funds are also the same in both cases.

The paper considers a single utility company's long‐ and medium‐term hydropower planning. The uncertainties are from the electricity forward curve and a random inflow. A simple and intuitive parameterization is given for the optimal production strategy. The accuracy of the parameterization is analysed by comparing its expected cash flows with the corresponding upper bound. In a test case the proposed method is compared with the realized production strategy of a Norwegian hydropower producer during winters 1997–2003. The parameterization gives earnings that are within 2.6% from the theoretical upper bound. Further, the results illustrate that during some years, part of the realized production strategy can be explained with the method, suggesting that during these years the forward curve information has already been incorporated in the production planning. However, even during the years when the correlation between the proposed strategy and the realized production is low, the strategy would have increased t...

In many democratic countries, the timing of elections is flexible. We explore this potentially valuable option using insights from option pricing in finance. The paper offers three main contributions on this problem. First, we derive a rationally-based mean-reverting political support process for the parties, assuming that politically heterogeneous voters continuously learn over time about evolving party fortunes. We solve for the long-run density for this process and derive the polling process from it by adding polling noise. Second, we explore optimal timing using the political support process. The incumbent sees its poll support, and must call an election within five years of the last election to maximize its expected total time in office. This resembles the optimal exercise rule for an American financial option. This option is recursive, and the waiting and stopping values subtly interact. We prove the existence of the optimal exercise rule in this setting, and show that the expected longevity is a convex-thenconcave function of the political support. Our model is tractable enough that we can analytically derive how the exercise rule responds to parametric shifts. We calibrate our model to the Labour-Tory rivalry in the U.K., with polling data from 1943-2005 and the 16 elections after 1945. Excluding three elections essentially forced by weak governments, our maximizing story quite well explains when the elections were called, and beats simple linear regressions. We also measure the value of election options, finding that over the long run they should more than double the expected time in power of a fixed term electoral cycle.

We consider the partial hedging of stochastic electricity load pattern with static forward strategies. We assume that the company under consideration maximizes the risk adjusted expected value of its electricity cash flows. First, we calculate an optimal hedge ratio and after that we use this hedge ratio to solve the optimal hedging time. Our results indicate, for instance that agents with high load volatility hedge later than agents that have low load volatility. Moreover, negative correlation between forwards and electricity load pattern postpones the hedging timing.

Electricity is one of the most important commodities for both consumers and producers, and it is subject to sharp variations in supply and demand, sometimes within a single day. But it is also one of the most difficult commodities on which to trade derivatives, because electricity is virtually unstorable. This has given rise to contracts such as the “swing option,” which sets minimum and maximum values for both the amount of power to be purchased in each period and also the cumulative amount of electricity purchased over the life of the contract. A swing option thus entails complex timing options with regard to fulfillment of the required minimum cumulative quantity purchased, and price-related options that let the holder buy more when the market price is above the option9s strike price, all constrained by the limits on maximum instantaneous and cumulative consumption. In this article, Keppo describes the decision process and presents a swing option valuation model based on simple electricity forwards and options. The use of the approach is illustrated with a couple of examples based on Nord Pool electricity prices.

This paper considers arbitrage-free option pricing in the presence of large agents. These large agents have a significant market power, and their trading strategies influence the dynamics of the financial asset prices. First, a simple asset pricing model in the presence of large agents is presented. Then a nonlinear partial differential equation is found for the prices of European options in the model. The unit option price depends on the large agent's asset holdings. Finally, a game model is introduced for the interaction between different market players. In this game, the outstanding number of options, as well as the option price, is found as a Nash equilibrium.

This paper studies an electricity producer's long-term optimality in the case of a multireservoir hydropower system. The model solves the optimal production process and trading strategy of electricity and weather derivatives by maximizing the utility from production and terminal water reservoir level. The optimal trading strategy hedges the rainfall and electricity price uncertainties.

We consider the valuation and rational exercise of irreversible investment opportunities in the presence of revenue uncertainty and delivery lags. In order to capture supply side market imperfections in the markets for investment goods, we assume that the lag depends on the revenue process faced by the investor. We show that such imperfections have a pronounced decelerating impact on rational investment demand as they may increase the value of waiting in excess of the exercise payoff even for projects which otherwise would be perceived as highly remunerative. We also consider the comparative static properties of the optimal investment policy and its value, and demonstrate that typically increased uncertainty decreases the investment incentives by increasing the value of waiting.

In many countries electricity supply business has been opened for competition. In this paper we analyze the problem of pricing of electricity tariffs in these open markets, when both the customers' electricity consumption and the market price are stochastic processes. Specifically, we focus on regular tariff contracts which do not have explicit amounts of consumption units defined in the contracts. Therefore the valuation process of these contracts differs from the valuation of electricity futures and options. The results show that the more there is uncertainty about the customer's consumption, the higher the fixed charge of the tariff contract should be. Finally, we analyze the indication of our results to the different methods for estimating the customer's consumption in the competitive markets. Since the consumption uncertainties enter into the tariff prices, the analysis indicates that the deterministic standard load curves do not provide efficient methods for evaluating the customers' consumption in competitive markets.

We introduce "indifference price" as the risk-adjusted unit price a supplier should charge for its customer’s random demand, given its flexible but limited capacity. The gap between this indifference price and the unit price used in practice, which is not adjusted for risk, then gives a hidden discount received by the supplier’s customers. Calibrating our model using a data set of a Norwegian bumper beam supplier, we show that this hidden discount rises in the customer’s order size. Further, customers with more volatile orders receive higher discount.

We examine the optimal portfolio selection problem of a single agent who receives an unhedgeable endowment. The agent wishes to optimize his/her log-utility derived from his/her terminal wealth. We do not solve this problem analytically but construct a recursive computational algorithm which approximates the optimal one. We present an intelligent initial portfolio which requires, numerically, about 25% fewer corrective steps in the algorithm than a random initial portfolio, and outperforms the portfolio which ignores the unhedgeable risk of the endowment.

We present a modeling framework for the analysis of investments in an oligopoly market for a homogenous commodity. The demand evolves stochastically and the firms carry out investment projects in order to adjust their production cost functions or production capacities. The model is formulated as a discrete time state-space game where the firms use feedback strategies. The firms are assumed to move sequentially to ensure a unique Markov-perfect Nash equilibrium. Once the equilibrium has been solved, Monte Carlo simulation is used to form probability distributions for the firms' cash flow patterns and accomplished investments. Such information can be used to value firms operating in an oligopoly market. An example of the model is given in a duopoly market. The example illustrates the trade-off between the value of flexibility and economies of scale under competitive interaction.

Most of the literature on real options considers the optimal decision of a firm in isolation from competitors. In reality, however, the actions of competing firms often affect each other's investment opportunities. We develop a game model where many firms compete for a single investment opportunity. When one of the firms triggers the investment the opportunity is completely lost for the other firms. The value of the project for the firms is assumed to follow a geometric Brownian motion. The model combines game theory and the theory of irreversible investment under uncertainty. We characterize the resulting Nash equilibrium under different assumptions on the information that the firms have about each other's valuations for the project. As an example, we present a case of building a telecommunications network.