scholarly journals The Present Value of a Series of Cashflows: Convergence in a Random Environment

1995 ◽  
Vol 25 (2) ◽  
pp. 81-94 ◽  
Author(s):  
Andrew J. G. Cairns
Keyword(s):  
Interest Rate ◽  
Random Environment ◽  
General Class ◽  
Almost Sure Convergence ◽  
Sufficient Condition ◽  
Rate Process ◽  
Present Value ◽  
The Interest Rate

AbstractThe present paper considers the present value, Z(t), of a series of cashflows up to some time t. More specifically, the cashflows and the interest rate process will often be stochastic and not necessarily independent of one another or through time. We discuss under what circumstances Z(t) will converge almost surely to some finite value as t→∞. This problem has previously been considered by Dufresne (1990) who provided a sufficient condition for almost sure convergence of Z(t) (the Root Test) and then proceeded to consider some specific examples of such processes. Here, we develop Dufresne's work and show that the sufficient condition for convergence can be proved to hold for quite a general class of model which includes the growing number of Office Models with stochastic cashflows.

Markov Branching Decision Chains with Interest-Rate-Dependent Rewards

1995 ◽  
Vol 9 (1) ◽  
pp. 99-121 ◽  
Author(s):  
Ying Huang ◽  
Arthur F. Veinott
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Optimal Policy ◽  
Linear Program ◽  
Present Value ◽  
Constraint Matrix ◽  
Rate Dependent ◽  
Markov Decision ◽  
The Interest Rate ◽  
The One

Finite-state-and-action Markov branching decision chains are studied with bounded endogenous expected population sizes and interest-rate-dependent one-period rewards that are analytic in the interest rate at zero. The existence of a stationary strong-maximum-present-value policy is established. Miller and Veinott's [1969] strong policy-improvement method is generalized to find in finite time a stationary n-present-value optimal policy and, when the one-period rewards are rational in the interest rate, a stationary strong-maximum-present-value policy. This extends previous studies of Blackwell [1962], Miller and Veinott [1969], Veinott [1974], and Rothblum [1974, 1975], in which the one-period rewards are independent of the interest rate, and Denardo [1971] in which semi-Markov decision chains with small interest rates are studied. The problem of finding a stationary n-present-value optimal policy is also formulated as a staircase linear program in which the objective function and right-hand sides, but not the constraint matrix, depend on the interest rate, and solutions for all small enough positive interest rates are sought. The optimal solutions of the primal and dual are polynomials in the reciprocal of the interest rate. A constructive rule is given for finding a stationary n-present-value optimal policy from an optimal solution of the asymptotic linear program. This generalizes the linear programming approaches for finding maximum-reward-rate and maximum-present-value policies for Markov decision chains studied by Manne [1960], d'Epenoux [1960, 1963], Balinski [1961], Derman [1962], Denardo and Fox [1968], Denardo [1970], Derman and Veinott [1972], Veinott [1973], and Hordijk and Kallenberg [1979, 1984].

scholarly journals Bounds for the Ruin Probability of a Discrete-Time Risk Process

2009 ◽  
Vol 46 (01) ◽  
pp. 99-112 ◽  
Author(s):  
Maikol A. Diasparra ◽  
Rosario Romera
Keyword(s):  
Markov Chain ◽  
Interest Rate ◽  
Discrete Time ◽  
Ruin Probability ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Proportional Reinsurance ◽  
Rate Process ◽  
Stationary Policy ◽  
The Interest Rate

We consider a discrete-time risk process driven by proportional reinsurance and an interest rate process. We assume that the interest rate process behaves as a Markov chain. To reduce the risk of ruin, we may reinsure a part or even all of the reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a stationary policy. To illustrate these results, a numerical example is included.

scholarly journals Additional costs to Finnish dairy farms due to occupational safety and health

1988 ◽  
Vol 60 (2) ◽  
pp. 81-86
Author(s):  
Tapio Klen
Keyword(s):  
Interest Rate ◽  
Annual Cost ◽  
Occupational Safety ◽  
Dairy Farms ◽  
Maintenance Cost ◽  
Present Value ◽  
Total Cost ◽  
Safety And Health ◽  
Additional Costs ◽  
The Interest Rate

The additional costs incurred by work safety measures to dairy farms were estimated by interviewing 95 dairy farmers and inspecting with them production buildings, machines and the need for personal protective devices at a commune. The present value of the implemented safety and health improvements rose to FIM 22 000 per farm in 1983. About FIM 17000 were due to the tractors, FIM 3 000 to the cow houses and FIM 2 000 to other machines and tools than tractors. The protective equipment of tractors caused the annual maintenance cost of FIM 4 350 and cow house FIM 650, if the interest rate were 10 %. The annual total cost was over FIM 6 000. The replacement value would have been about FIM 31 000 in 1983. If all deficiences still remaining in 1983 had been corrected at once, the total cost would have been about FIM 12000 per farm, which leads to an annual cost of FIM 3 100. As for still remaining deficiencies, the study suggested need for an annual cost of about FIM 1 500 due to personal protectors. Half of this sum was due to need for the acquisition of personal safety equipment for forest work. Correcting the safety and health deficiencies of the cowshed and agricultural machines would produce each an annual cost of about FIM 800 per farm. The present value of the labor protection investments in 1983 was FIM 22 000 per farm, and there still remained need to invest an additional FIM 12000 in order to eliminate the remaining deficiencies. So, the theoretical total of the annual maintenance cost would have been FIM 6 600—9 200 per farm depending on the interest rate. Because the study concerned only one commune, the results cannot be generalized to the whole country.

Liquidity: Its Origins and Implications in an Uncertain Multiperiod World with Limited Borrowing

1994 ◽  
Vol 38 (1) ◽  
pp. 36-46
Author(s):  
Edward Miller
Keyword(s):  
Interest Rate ◽  
Time Preference ◽  
Market Value ◽  
Cash Flows ◽  
Present Value ◽  
Capital Productivity ◽  
Inside Money ◽  
Future Consumption ◽  
Lending Rates ◽  
The Interest Rate

If borrowing rates exceed lending rates, liquid assets are held to provide an option on future consumption. The rate of time preference exceeds the interest rate. Thus the market value of marketable securities exceeds the present value at the rate of time preference of their cash flows. The interest rate is determined not merely by time preference and capital productivity, but is a number calculated from the values of liquid assets. Inside money has an impact.

scholarly journals Negative interest rates: why and how?

2017 ◽  
Vol 67 (5) ◽  
Author(s):  
Jozef Kisel’ák ◽  
Philipp Hermann ◽  
Milan Stehlík
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Great Depression ◽  
Banking Sector ◽  
Second Order ◽  
Rate Process ◽  
Practical Realization ◽  
The Great Depression ◽  
Negative Interest Rates ◽  
The Interest Rate

AbstractInterest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929–39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and practical ideas how to model and eventually overcome empirical negative rates can be suggested, however, they are far beyond a simple practical realization. In this paper we discuss the dynamical reasons why negative interest rates can happen in the second order differential dynamics and how they can influence the variance and expectation of the interest rate process. Such issues are highly practical, involving e.g. the banking sector and pension securities.

scholarly journals Bounds for the Ruin Probability of a Discrete-Time Risk Process

2009 ◽  
Vol 46 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Maikol A. Diasparra ◽  
Rosario Romera
Keyword(s):  
Markov Chain ◽  
Interest Rate ◽  
Discrete Time ◽  
Ruin Probability ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Proportional Reinsurance ◽  
Rate Process ◽  
Stationary Policy ◽  
The Interest Rate

We consider a discrete-time risk process driven by proportional reinsurance and an interest rate process. We assume that the interest rate process behaves as a Markov chain. To reduce the risk of ruin, we may reinsure a part or even all of the reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a stationary policy. To illustrate these results, a numerical example is included.

scholarly journals Profitability of growing Scots pine on cutaway peatlands

Silva Fennica ◽  
2020 ◽  
Vol 54 (3) ◽  
Author(s):  
Lasse Aro ◽  
Anssi Ahtikoski ◽  
Jyrki Hytönen
Keyword(s):  
Interest Rate ◽  
Scots Pine ◽  
Net Present Value ◽  
Northern Region ◽  
Land Values ◽  
Present Value ◽  
Annual Increment ◽  
Stand Management ◽  
Pine Trees ◽  
The Interest Rate

A major after-use option for former peat harvesting areas has been afforestation. The profitability of afforestation with Scots pine trees ( L.) was studied in two 31–32-year old experiments in southern and northern Finland. The stands were established by seeding and planting, and various fertilization treatments and drainage intensities were tested. The financial performance for each plot was assessed in three steps. First, the costs occurred during the measurement time were summed up according to their present value. Then, for the rest of the rotation (i.e., from the age of 31/32 onwards) the stand management was optimized in order to maximize the net present value (MaxNPV). Finally, bare land values (BLVs) were calculated by summing up the present value of costs and the MaxNPV and converting the sum of the series into infinity. The afforestation method did not affect the mean annual increment (MAI; 9.2–9.5 m ha a) in the southern experiment. In the northern experiment the afforestation method, ditch spacing and fertilization had significant effects on the MAI of the stands. The average MAI of the planted pines was 8.9 m ha a, and for seeded pines it was 7.5 m ha a. The BLV at an interest rate of 3% was positive for all stands in both regions. In the northern region afforestation method, ditch spacing and fertilization also had a significant effect on the BLV. When the interest rate was 5%, almost two thirds of the stands had a negative BLV in both regions.Pinus sylvestris3–1–13–1–13–1–1

The Role of Different Channels in Transmitting Monetary Policy into Output and Price in Vietnam

2015 ◽  
pp. 20-40
Author(s):  
Vinh Nguyen Thi Thuy
Keyword(s):  
Monetary Policy ◽  
Exchange Rate ◽  
Interest Rate ◽  
Money Supply ◽  
Monetary Transmission ◽  
Impulse Response Functions ◽  
Short Run ◽  
The Exchange Rate ◽  
The Interest Rate ◽  
Interest Rate Channel

The paper investigates the mechanism of monetary transmission in Vietnam through different channels - namely the interest rate channel, the exchange rate channel, the asset channel and the credit channel for the period January 1995 - October 2009. This study applies VAR analysis to evaluate the monetary transmission mechanisms to output and price level. To compare the relative importance of different channels for transmitting monetary policy, the paper estimates the impulse response functions and variance decompositions of variables. The empirical results show that the changes in money supply have a significant impact on output rather than price in the short run. The impacts of money supply on price and output are stronger through the exchange rate and credit channels, but however, are weaker through the interest rate channel. The impacts of monetary policy on output and inflation may be erroneous through the equity price channel because of the lack of an established and well-functioning stock market.

DETERMINAN INFLASI DI INDONESIA PERIODE 1980-2015

2016 ◽  
Vol 21 (1) ◽  
pp. 1-7
Author(s):  
Risna Risna
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Money Supply ◽  
Government Spending ◽  
Positive Impact ◽  
Secondary Data ◽  
Quantitative Approach ◽  
State Spending ◽  
Factors Affecting ◽  
The Interest Rate

This study aims to determine the effect of government spending, the money supply, the interest rate of Bank Indonesia against inflation.This study uses secondary data. Secondary data were obtained directly from the Central Bureau of Statistics and Bank Indonesia. It can be said that there are factors affecting inflationas government spending, money supply, and interest rates BI. The reseach uses a quantitative approach to methods of e-views in the data. The results of analysis of three variables show that state spending significantand positive impact on inflationin Indonesia, the money supply significantand negative to inflationin Indonesia, BI rate a significantand positive impact on inflation in Indonesia

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