Decisions such as saving, investing, policymaking, have consequences in multiple time
periods and are called intertemporal. These choices require decision-makers to trade-off costs and benefits at different points in time. Time preference is the preference
for immediate gratification or utility over delayed gratification. The discount rate is
a tool used to measure this psychological phenomenon.
This thesis considers the problem of an individual maximizing his utility from
consumption and final wealth when his discount rate is not constant. The question
we answer is the following: if we allow the individual to update his decisions, will he
stick to his original strategy or will he switch?
We show that there are cases in which the individual's strategy keeps changing
thus his behaviour becomes time inconsistent. In Chapter 1, we introduce two notions
to solve this inconsistency problem: The agent can pre commit i.e. he does not
change his original optimal strategy. The agent can also plan for his future changes of
strategy and adopt time consistent strategies also known as subgame perfect strategies.
We also review the existing literature on time discounting and time consistency.
Chapter 2 considers the time consistency in the expected utility maximization
problem. The risk preference is of the Constant Relative Risk Aversion (CRRA) type,
the time preference is specified by a non constant discount rate and we allow the volatility of the stock price to be stochastic. We show that the determination of one
quantity: the utility weighted discount rate completely characterizes the individual's
subgame perfect strategies.
Chapter 3 is about equilibrium pricing in a model populated by several economic
agents in a complete financial market. These agents are investing, saving
and consuming and want to maximize their expected utility of consumption and
final wealth. We allow the economic agents to differ in their risk preferences, beliefs
about the future of the economy and in their time preferences (non constant discount
rates). Since the optimal strategies are time inconsistent, the equilibrium is
computed by using the time 0 optimal ( precommitment) strategies for the market
clearing conditions.
Chapter 4 considers the same model as chapter 2. We solve the equilibrium
problem when time consistent strategies are used for the market clearing conditions.
We limit the study to two economic agents. The subgame perfect equilibrium is
compared to the optimal equilibrium of Chapter 3. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/23890 |
| Date | January 2018 |
| Creators | Mbodji, Oumar |
| Contributors | Pirvu, Traian, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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