Here is something you can use that is practical, low toxicity to humans and pets, and not too difficult to use.

First, (and this is the most difficult part) you need to get your hands on some boric acid. The Japanese for it is: ホウ酸. You can find it in a drugstore which looks like this. Or, you might be able to find a large plastic cannister of it especially for use as an insecticide in both drugstores and DIY stores which looks like this (around Y600 at most).

Second, read how to effectively use boric acid. This is decent. In some cases, you are trying to get it into the various hiding places like cracks and crevices. In other cases, if you live in a house where they are coming in from the outside, the powder is cheap and plentiful enough to create a white perimeter defence around your home.

Third, learn how to make effective cockroach bait using boric acid powder. This "recipe" from Hawaii:

"We make a mixture of 1/3 boric acid, 1/3 cornmeal and 1/3 granular white sugar.

"Then we take a tin can and put two or three holes in the sides at the base of the can. Next, we put a tablespoon of the mixture into the can and cover the top with a piece of aluminum foil.

"We put these everywhere that the cockroaches are, but out of the way of pets and children.

"This mixture never goes bad and works very well for us. I find dead cockroaches nearly every day in our house using cans that contain mixtures that are 10-15 years old."

Boric acid is "hosan" in Japanese and cornmeal is "kohnmiiru."

There is no particular time of the year that Asian cockroaches produce eggs, and females can sometimes be seen carrying egg capsules that contain around 40 eggs.

The females drop the capsule before the young hatch. Development from eggs to adults takes three to four months, and cockroaches can live up to a year. Females can produce up to eight egg cases in a lifetime -- that can mean 300-400 offspring!